Faculty Appointments

Centennial Professor of Mathematics
Centennial Professor of MathematicsProfessor of Molecular Physiology and Biophysics

Education

Ph.D., Mathematics, University of Texas, Austin, TexasB.A., UniversitÃ degli Studi di Firenze, Florence, Italy

Office Address

1416 Stevenson Center

Nashville, TN 37240

Nashville, TN 37240

Research Description

Mathematical Biology; Signal Transduction; Biophysics of Motion of Second Messengers; Cell Cycle; Complexity in Endothelial Cell Signaling; Mathematical Homogenization and Concentrated Capacity in Visual Transduction; Partial Differential Equations of Elliptic and Parabolic Type; Degenerate and Singular Equations; Local and Global Behaviour of Solutions; Harnack-Type Estimates; Calculus of Variations; Quasi-Minima; Potential Theory; Phase Transition; Free Boundary Problems; Fluid Dynamics; Conduction-Convection; Navier Stokes Equations; Motion in Porous Media; Ill-Posed Problems; Thin Film Dynamics; Classical Mechanics.

Research Keywords

Mathematical Biology; Signal Transduction; Biophysics of Motion of Second Messengers; Cell Cycle; Complexity in Endothelial Cell Signaling; Mathematical Homogenization and Concentrated Capacity in Visual Transduction; Partial Differential Equations of Elliptic and Parabolic Type; Degenerate and Singular Equations; Local and Global Behaviour of Solutions; Harnack-Type Estimates; Calculus of Variations; Quasi-Minima; Potential Theory; Phase Transition; Free Boundary Problems; Fluid Dynamics; Conduction-Convection; Navier Stokes Equations; Motion in Porous Media; Ill-Posed Problems; Thin Film Dynamics; Classical Mechanics.

Publications

D. Andreucci, P. Bisegna and E.DiBenedetto. Homogenization and Concentration of Capacity in the Rod Outer Segment with Incisures (invited paper to the memory of C. Pucci ).

D. Andreucci and E. DiBenedetto. L estimates for the gradient of Solutions of the Flow by Mean Curvature.

H. Khanal, V. Alexiades and E.DiBenedetto. Response of Dark-Adapted Retinal Rod Photoreceptors.

E. DiBenedetto, J. M. Urbano and V. Vespri. Current Issues on Singular and Degenerate Evolution Equations (Invited book Chapter).

H.Khanal, V. Alexiades, G. Caruso, F. Rieke, H. E. Hamm and E.DiBenedetto. Mathematical and Numerical Modeling of Spatio-temporal Signaling in Rod Phototransduction.

D. Andreucci, P. Bisegna and E.DiBenedetto. Homogenization and Concentrated Capacity for the Heat Equation wih non Linear Variational Data in Reticular Almost Disconnected Structures, and Applications to Visual Transduction.

H. Khanal, V. Alexiades, H. Hamm and E.DiBenedetto. Numerical Simulations of diffusion of Second Messengers cGMP and Ca2+ in Rod Photoreceptors.

D. Andreucci, P. Bisegna, H.E. Hamm and E.DiBenedetto. # Mathematical Model of the Spatio-Temporal Dynamics of Second Messengers in Visual Transduction.

D. Andreucci, P. Bisegna and E.DiBenedetto. Homogenization and Concentrated Capacity in Reticular Almost Disconnected Structures.

D. Andreucci, G. Caruso and E. DiBenedetto. Fingering in a Hele-Shaw Cell as an Obstacle like problem.

G.Q. Cheng and E. DiBenedetto. Stability of Entropy Solutions to the Cauchy Problem for a Class of Hyperbolic-Parabolic Equations.

E. DiBenedetto and D. Diller. Singular Semiliniear Elliptic equations in L1(IRN).

E. DiBenedetto and G. Alessandrini. Determining 2-Dimensional Cracks in 3-Dimensional Bodies: Uniqueness and Stability.

E. DiBenedetto. Parabolic Equations with Multiple Singularities or Degeneracies.

E. DiBenedetto and D. Diller. A New Form of the Sobolev Multiplicative Inequality and Applications to the Asymptotic Decay if Solutions to the Neuman Problem for Quasilinear Parabolic Equations with Measurable Coefficients.

E. Dibenedetto, D. Diller and S. Davis. Some a priori Estimates for a Singular Evolution Equation Arising in Thin Film Dynamics.

S. Davis, E.DiBenedetto and D. Diller. XSome a Priori Estimates for a Singular Evolution Equation Arising in Thin Film Dynamics.

E.DiBenedetto and D. Diller. On the Asymptotic Behavior of Drying a Photographic Film.

E. DiBenedetto and V. Vespri. On the Singular Equation B(u)t=Du.

E.DiBenedetto and V. Vespri. On the Singular Equation b(u)t=Delta u.

E.DiBenedetto and M. O'Leary. Conduction-Convection problems with Change of Phase.

E.DiBenedetto and D. Diller. About a Singular Parabolic Equation arising in Thin Film Dynamics and in the Ricci Flow for Complete R2.

E.DiBenedetto. Degenerate and Singular Parabolic Equations.

E.DiBenedetto and V. Vespri. Continuity for Bounded Solutions of Multiphase Stefan Problem.

E. DiBenedetto and J. Manfredi. On the Higher Integrability of the Gradient of Weak SOlutions of Certain Degenerate Elloptic Equations.

Y.Z. Chen and E. DiBenedetto. On the Harnack Inequality for Nonnegative Solutions of Singular Parabolic Equations, Degenerate Diffusion.

E. DiBenedetto and M. O'Leary. Three-Dimensional Conduction-Convection with Change of Phase.

E.DiBenedetto and M. O'Leary. Local Ca Convergence of the Elliptic Regularizations of Parabolic Equations (invited paper for the 70th birthday of G. Sestini).

D. Andreucci and E. DiBenedetto. Weak Solutions of Equations of the Type of Nonlinear Filtration.

E. DiBenedetto and Y. C. Kwong. Harnack Estimates and Extinction Profile for Weak Solutions of Certain Singular Parabolic Equations, Trans.

E. DiBenedetto and Chen Ya-A-Zhe. Holder Estimates of Solutions of Singular Parabolic Equations with Measurable Coefficients.

E. DiBenedetto, Y. C. Kwong and V. Vespri. Local Analiticity and Asymptotic Behaviour of Solutions of Certain Singular Parabolic Equations.

D.Andreucci and E.DiBenedetto. Behaviour at Infinity of Solutions of Certain Degenerate Evolution Equations with Strongly Nonlinear Sources. Annali Scuola Normale Superiore di Pisa.

E.DiBenedetto, Y.C.Kwong and V.Vespri. Local Analiticity and Asymptotic Behaviour of Solutions of Certain Singular Parabolic Equations.

D.Andreucci and E.DiBenedetto. A New Approach to Initial Traces in Nonlinear Filtration.

E.DiBenedetto and M.A. Herrero. Nonnegative Solutions of the Evolution p-Laplacian Equation; Initial Traces and Cauchy Problem when p (1,2).

T.Battacharya E.DiBenedetto and J.Manfredi. # Limits as p->\infty of Deltap up=f, and Extremal Problems in W{1,infty}.

E.DiBenedetto and Chen Ya-zhe. Boundary Estimates for Solutions of Nonlinear Degenerate Parabolic Systems.

E.DiBenedetto and M.A. Herrero. On the Cauchy Problem and Initial Traces for a Degenerate Parabolic Equation.

E.DiBenedetto. Local Regularity and Extinction Free Boundary for a Singular Parabolic Equation.

E.DiBenedetto. Initial Traces for Degenerate and Singular Evolution Equations, #, (), ;.

E.DiBenedetto and Chen Ya-zhe. On the Local Behaviour of Solutions of Singular Parabolic Equations.

E.DiBenedetto. Harnack Estimates in Certain Function Classes (invited paper for the 70th of Renato Nardini).

E.DiBenedetto. Harnack Type Inequalities for Some Degenerate Parabolic Equations.

E. DiBenedetto and R. Gariepy. On the Local Behavior of Solutions for an Elliptic-Parabolic Equation.

E.DiBenedetto. Intrinsic Harnack--Type Inequalities, for Solutions of Degenerate Parabolic Equations.

E.DiBenedetto. On the Local Behavior of Solutions of Degenerate Parabolic Equations with Measurable Coefficients.

E.DiBenedetto and A. Friedman. Bubble Growth in Porous Media.

E.DiBenedetto C. Elliot and A. Friedman. The Free Boundary of a Flow in a Porous Body Heated from its Boundary.

E.DiBenedetto. A Boundary Modulus of Continuity for a Class of Singular Parabolic Equations.

E.DiBenedetto and A. Friedman. Periodic Behavior of Solutions for the Evolutionary Dam Problem and Related Free Boundary Problems.

E.DiBenedetto and A. Friedman. Conduction-Convection with a Change of Phase.

H.W. Alt and E.DiBenedetto. Non Steady Flow of Water and Oil Through Inhomogeneous Porous Media.

E. DiBenedetto. The Flow of Two Immiscible Fluids Through a Porous Medium; Regularity of the Saturation.

E.DiBenedetto. Periodic Solutions of the Dam Problem.

E.DiBenedetto. Remarks on Some Ill Posed Problems.

E.DiBenedetto and C. Elliott. Existence for a Problem in Ground Freezing.

E.DiBenedetto and A. Friedman. H"older Estimates for Nonlinear Degenerate Parabolic Systems.

E.DiBenedetto, A. Fasano and M. Primicerio. On a Free Boundary Problem Related to an Irreversible Process.

E.DiBenedetto and N.S. Trudinger. Harnack Inequalities for Quasi-Minima of Variational Integrals.

E.DiBenedetto andf A. Friedman. The Ill-Posed Hele-Shaw Model and the Stefan Problem for Supercooled Water.

E.DiBenedetto and D. Hoff. An Interface Tracking Algorithm for the Porous Medium Equation.

E. DiBenedetto and A. Friedman. Regularity of Solutions of Nonlinear Degenerate Parabolic Systems.

H.W. Alt and E.DiBenedetto. Flow of Oil and Water Through Porous Media.

E.DiBenedetto. Conduction-Convection Problems with Change of phase, Conduction-Convection Problems with Change of phase.

E. DiBenedetto and R.E. Showalter. Free Boundary Problems for a Degenerate Parabolic System.

E.DiBenedetto. Continuity of Weak Solutions to a General Porous Medium Equation.

E. DiBenedetto and R. Spigler. An Algorithm for the One Phase Stefan Problem.

J.R. Cannon E. DiBenedetto and K.G. Knightly. The Bidimensional Stefan Problem with Convection: The Time Dependent Case.

E.DiBenedetto. Local Regularity of Weak Solutions of Degenerate Elliptic Equations.

E.DiBenedetto. Change of Phase with Convection.

E.DiBenedetto. Continuity of Weak Solutions to Certain Singular Parabolic Equations.

E.DiBenedetto and R.E. Showalter. A Pseudo-Parabolic Variational Inequality and Stefan Problem.

E. DiBenedetto. Continuity for Singular Parabolic Equations.

E.DiBenedetto. Continuity for Singular Parabolic Equations.

E. DiBenedetto and M. Pierre. On the Maximum Principle for Pseudo-Parabolic Equations.

E. DiBenedetto. Interior and Boundary Regularity for a Class of Free Boundary Problems.

E. DiBenedetto and R.E. Showalter. Implicit Degenerate Evolution Equations and Applications.

J.R. Cannon , E.DiBenedetto and G.K. Knightly. The Steady State Stefan Problem with Convection.

J.R. Cannon and E.DiBenedetto. On the Existence of Weak Solutions to an n-dimensional Stefan Problem with Nonlinear Boundary Conditions.

E. DiBenedetto. Regularity Results for the two Phase N-dimensional Stefan Problem.

E.DiBenedetto. The Initial Value Problem for the Boussinesq Equations with Data in Lp.

J.R. Cannon and E.DiBenedetto. The Steady State Stefan Problem with Convection with Mixed Temperature and Nonlinear Boundary Conditions.

G. Borgioli and M. Ughi and E.DiBenedetto. Stefan Problems with Nonlinear Boundary Conditions: The Polygonal Method.

J.R. Cannon and E.DiBenedetto. On the Existence of Solutions of Boundary Value Problems in Fast Chemical Reactions.

D. Andreucci, G. Caruso and E.DiBenedetto. Ill-Posed Hele-Shaw Flows.

__Applicable Analysis__. 2005; (()).D. Andreucci and E. DiBenedetto. L estimates for the gradient of Solutions of the Flow by Mean Curvature.

__Preprint__. 2004; (()).H. Khanal, V. Alexiades and E.DiBenedetto. Response of Dark-Adapted Retinal Rod Photoreceptors.

__Proceedings of Dynamical Systems and Applications, M.Sambandham, Dynamic Publishers__. 2004; 4: 138-45.E. DiBenedetto, J. M. Urbano and V. Vespri. Current Issues on Singular and Degenerate Evolution Equations (Invited book Chapter).

__Handbook of Differential Equations Elsevier Pub., Edited by C. Dafermos and E. Feireisl__. 2004; 1: 169-286.H.Khanal, V. Alexiades, G. Caruso, F. Rieke, H. E. Hamm and E.DiBenedetto. Mathematical and Numerical Modeling of Spatio-temporal Signaling in Rod Phototransduction.

__Preprint__. 2004.D. Andreucci, P. Bisegna and E.DiBenedetto. Homogenization and Concentrated Capacity for the Heat Equation wih non Linear Variational Data in Reticular Almost Disconnected Structures, and Applications to Visual Transduction.

__Annali di Matematica Pura e Applicata__. 2003; 4((182)): 375-407.H. Khanal, V. Alexiades, H. Hamm and E.DiBenedetto. Numerical Simulations of diffusion of Second Messengers cGMP and Ca2+ in Rod Photoreceptors.

__American Inst. of Physics__. 2003; 665(()): 165-72.D. Andreucci, P. Bisegna, H.E. Hamm and E.DiBenedetto. # Mathematical Model of the Spatio-Temporal Dynamics of Second Messengers in Visual Transduction.

__Biophysical Journal__. 2003; 85: 1358-76.D. Andreucci, P. Bisegna and E.DiBenedetto. Homogenization and Concentrated Capacity in Reticular Almost Disconnected Structures.

__Comptes Rendus Acad. des Sciences Paris__. 2002; 4((Ser. I, 335)): 329-32.D. Andreucci, G. Caruso and E. DiBenedetto. Fingering in a Hele-Shaw Cell as an Obstacle like problem.

__Indiana Univ. Math. Journal__. 2000; 49((4)): 1287-321.G.Q. Cheng and E. DiBenedetto. Stability of Entropy Solutions to the Cauchy Problem for a Class of Hyperbolic-Parabolic Equations.

__SIAM J. on Math. Analysis__. 2000; 33((44)): 751-62.E. DiBenedetto and D. Diller. Singular Semiliniear Elliptic equations in L1(IRN).

__Non-Linear Diff. Equ. and their Appl. Vol. #, pp.; Birkhauser. Invited paper for the H. Amann Anniversary Volume__. 1998; 35(()): 143-82.E. DiBenedetto and G. Alessandrini. Determining 2-Dimensional Cracks in 3-Dimensional Bodies: Uniqueness and Stability.

__Indiana Univ. Math. J__. 1997; 46((1)): 1-82.E. DiBenedetto. Parabolic Equations with Multiple Singularities or Degeneracies.

__Equadiff__. 1997; 9: 25-48.E. DiBenedetto and D. Diller. A New Form of the Sobolev Multiplicative Inequality and Applications to the Asymptotic Decay if Solutions to the Neuman Problem for Quasilinear Parabolic Equations with Measurable Coefficients.

__Nat. Acad. of Sciences of Ukraine, Nonlinear Boundary Value Problem__. 1997; 8(()): 81-8.E. Dibenedetto, D. Diller and S. Davis. Some a priori Estimates for a Singular Evolution Equation Arising in Thin Film Dynamics.

__SIAM J. on Math. Anal__. 1996; 27((3)): 638-60.S. Davis, E.DiBenedetto and D. Diller. XSome a Priori Estimates for a Singular Evolution Equation Arising in Thin Film Dynamics.

__SIAM Jour. Math. Anal__. 1996; 3((2)): 638-60.E.DiBenedetto and D. Diller. On the Asymptotic Behavior of Drying a Photographic Film.

__Advances in Diff. Equations__. 1996; 6((1)): 989-1003.E. DiBenedetto and V. Vespri. On the Singular Equation B(u)t=Du.

__Archive for Rat. Mech. Anal__. 1995; 132: 247-309.E.DiBenedetto and V. Vespri. On the Singular Equation b(u)t=Delta u.

__Archive for Rational Mechanics and Analysis__. 1995; ((132)): 247-309.E.DiBenedetto and M. O'Leary. Conduction-Convection problems with Change of Phase.

__Nonlinear Problems in Applied MathematicsSIAM special Volume, for the 70th birthday of I. Stackgold. Edited by T.S. Angell, L.P. Cook, R.E. Kleinman and W.E. Olmstead__. 1995; 104-15.E.DiBenedetto and D. Diller. About a Singular Parabolic Equation arising in Thin Film Dynamics and in the Ricci Flow for Complete R2.

__Lecture Notes in Pure and Applied Mathematics, Marcel Dekker New York,Special Volume for the 70th birthday of C. Pucci. Edited by G. Talenti, E. Vesentini and P. Marcellini__. 1995; 177: 103-20.E.DiBenedetto. Degenerate and Singular Parabolic Equations.

__Recent Advances in Partial Diff. Equ., J. Wiley, Research in Applied Mathematics, Editor P.G. Ciarlet__. 1994; 55-84.E.DiBenedetto and V. Vespri. Continuity for Bounded Solutions of Multiphase Stefan Problem.

__Rendiconti Accademia Nazionale dei Lincei__. 1994; 5((9)): 297-302.E. DiBenedetto and J. Manfredi. On the Higher Integrability of the Gradient of Weak SOlutions of Certain Degenerate Elloptic Equations.

__Amer. J. of Math__. 1993; 115((5)): 1107-34.Y.Z. Chen and E. DiBenedetto. On the Harnack Inequality for Nonnegative Solutions of Singular Parabolic Equations, Degenerate Diffusion.

__The IMA Volumes in Math. and its Appl__. 1993; 47 Springer(()): 61-9.E. DiBenedetto and M. O'Leary. Three-Dimensional Conduction-Convection with Change of Phase.

__Arch. Rat. Mech. Anal__. 1993; 123: 99-116.E.DiBenedetto and M. O'Leary. Local Ca Convergence of the Elliptic Regularizations of Parabolic Equations (invited paper for the 70th birthday of G. Sestini).

__Meccanica__. 1993; 28: 97-10.D. Andreucci and E. DiBenedetto. Weak Solutions of Equations of the Type of Nonlinear Filtration.

__Non Linear Anal. TMA__. 1992; 19((1)): 29-41.E. DiBenedetto and Y. C. Kwong. Harnack Estimates and Extinction Profile for Weak Solutions of Certain Singular Parabolic Equations, Trans.

__Amer. Math. Soc__. 1992; 330((2)): 783-811.E. DiBenedetto and Chen Ya-A-Zhe. Holder Estimates of Solutions of Singular Parabolic Equations with Measurable Coefficients.

__Arch. Rat. Mech. Anal__. 1992; 118(()): 257-71.E. DiBenedetto, Y. C. Kwong and V. Vespri. Local Analiticity and Asymptotic Behaviour of Solutions of Certain Singular Parabolic Equations.

__Indiana J. of Math__. 1991; 40((2)): 741-65.D.Andreucci and E.DiBenedetto. Behaviour at Infinity of Solutions of Certain Degenerate Evolution Equations with Strongly Nonlinear Sources. Annali Scuola Normale Superiore di Pisa.

__Annali Scuola Normale Superiore di Pisa__. 1991; XV(3)((Ser. IV)): 363-441.E.DiBenedetto, Y.C.Kwong and V.Vespri. Local Analiticity and Asymptotic Behaviour of Solutions of Certain Singular Parabolic Equations.

__Indiana Univ. Math. Jour__. 1991; 2((40)): 741-65.D.Andreucci and E.DiBenedetto. A New Approach to Initial Traces in Nonlinear Filtration.

__Ann. de l'Institut H. PoincarÃ©__. 1990; 4((7)): 305-34.E.DiBenedetto and M.A. Herrero. Nonnegative Solutions of the Evolution p-Laplacian Equation; Initial Traces and Cauchy Problem when p (1,2).

__Archive for Rational Mechanics and Analysis__. 1990; 3((1)): 225.T.Battacharya E.DiBenedetto and J.Manfredi. # Limits as p->\infty of Deltap up=f, and Extremal Problems in W{1,infty}.

__Rendiconti Seminario Matematico Univ. Torino__. 1989; ((Fasc. Spec.)): 15-68.E.DiBenedetto and Chen Ya-zhe. Boundary Estimates for Solutions of Nonlinear Degenerate Parabolic Systems.

__Jour. f"ur die Reine und Angewandte Mathematik__. 1989; ((395)): 102-31.E.DiBenedetto and M.A. Herrero. On the Cauchy Problem and Initial Traces for a Degenerate Parabolic Equation.

__Trans. Amer. Math. Soc__. 1989; 1((314)): 187-224.E.DiBenedetto. Local Regularity and Extinction Free Boundary for a Singular Parabolic Equation.

__Free Boundary Problems and Applications, Pitman; Edited by J. Sprekels and K.H. Hoffman__. 1988; 1-7.E.DiBenedetto. Initial Traces for Degenerate and Singular Evolution Equations, #, (), ;.

__Problems Involving Change of Type, Springer Lecture notes in Physics,Conf. for the 60th birthday of J. Hale; Edited by K. Kirchg"assner__. 1988; ((359)): 175-90.E.DiBenedetto and Chen Ya-zhe. On the Local Behaviour of Solutions of Singular Parabolic Equations.

__Archive for Rational Mechanics and Analysis__. 1988; 4((103)): 319.E.DiBenedetto. Harnack Estimates in Certain Function Classes (invited paper for the 70th of Renato Nardini).

__Atti Seminario Matematico e Fisico Univ. Modena__. 1988; XVI: 173-82.E.DiBenedetto. Harnack Type Inequalities for Some Degenerate Parabolic Equations.

__Nonlinear Diffusion Equations and Their Equilibrium States Mathematical Sciences Research Institute, Publ. Springer Edited by W.M. Ni, L.A. Peletier and J. Serrin__. 1987; ((12)): 267-72.E. DiBenedetto and R. Gariepy. On the Local Behavior of Solutions for an Elliptic-Parabolic Equation.

__Archive for Rational Mechanics and Analysis__. 1987; 1((97)): 1-17.E.DiBenedetto. Intrinsic Harnack--Type Inequalities, for Solutions of Degenerate Parabolic Equations.

__Archive for Rational Mechanics and Analysis__. 1987; 2((100)): 129-47.E.DiBenedetto. On the Local Behavior of Solutions of Degenerate Parabolic Equations with Measurable Coefficients.

__Annali Scuola Normale Superiore di Pisa__. 1986; Ser. IV((X3)): 487-535.E.DiBenedetto and A. Friedman. Bubble Growth in Porous Media.

__Indiana Univ. Math. Jour__. 1986; 3((35)): 573.E.DiBenedetto C. Elliot and A. Friedman. The Free Boundary of a Flow in a Porous Body Heated from its Boundary.

__Non Linear Analysis TMA__. 1986; 10: 879-900.E.DiBenedetto. A Boundary Modulus of Continuity for a Class of Singular Parabolic Equations.

__Journal of Differential Equations__. 1986; 3((63)): 418-47.E.DiBenedetto and A. Friedman. Periodic Behavior of Solutions for the Evolutionary Dam Problem and Related Free Boundary Problems.

__Comm. in Part. Diff. Eqs__. 1986; 12((11)): 1297-377.E.DiBenedetto and A. Friedman. Conduction-Convection with a Change of Phase.

__Journal of Differential Equations__. 1986; 2((62)): 129-85.H.W. Alt and E.DiBenedetto. Non Steady Flow of Water and Oil Through Inhomogeneous Porous Media.

__Annali Scuola Normale Superiore di Pisa__. 1985; XII(3)((Ser. IV)): 335-92.E. DiBenedetto. The Flow of Two Immiscible Fluids Through a Porous Medium; Regularity of the Saturation.

__Theory and Applications of Liquid Crystals, Springer Verlag Lecture Notes,Edited by D. Kinderlehrer and Ericksen__. 1985; 5(()): 123-43.E.DiBenedetto. Periodic Solutions of the Dam Problem.

__Nonlinear Evolution Equations: Qualitative Properties of Solutions, PitmanEdited by A. Tesei and L. Boccardo__. 1985; 149(()): 77-84.E.DiBenedetto. Remarks on Some Ill Posed Problems.

__Nonlinear PDEs, Australian Nat. Univ. Camberra, Edited by N. Trudinger and L. Simon__. 1985; (()): 32-56.E.DiBenedetto and C. Elliott. Existence for a Problem in Ground Freezing.

__Non Linear Analysis TMA__. 1985; 9((9)): 953-68.E.DiBenedetto and A. Friedman. H"older Estimates for Nonlinear Degenerate Parabolic Systems.

__Jour. f__. 1985; 357(()): 1-22.E.DiBenedetto, A. Fasano and M. Primicerio. On a Free Boundary Problem Related to an Irreversible Process.

__Control and Cybernetics__. 1985; 1-3((14)): 195-219.E.DiBenedetto and N.S. Trudinger. Harnack Inequalities for Quasi-Minima of Variational Integrals.

__Ann. de l'Institut H. PoincarÃ©__. 1984; 4((1)): 295-308.E.DiBenedetto andf A. Friedman. The Ill-Posed Hele-Shaw Model and the Stefan Problem for Supercooled Water.

__Trans. Amer. Math. Soc__. 1984; 1((T282)): 183-204.E.DiBenedetto and D. Hoff. An Interface Tracking Algorithm for the Porous Medium Equation.

__Trans. Amer. Math. Soc__. 1984; 2((284)): 463-500.E. DiBenedetto and A. Friedman. Regularity of Solutions of Nonlinear Degenerate Parabolic Systems.

__Jour. f"ur die Reine und Angewandte Mathematik__. 1984; ((349)): 83-128.H.W. Alt and E.DiBenedetto. Flow of Oil and Water Through Porous Media.

__Asterisque, Soc. Mathematique de France__. 1984; ((118,)): 89-108.E.DiBenedetto. Conduction-Convection Problems with Change of phase, Conduction-Convection Problems with Change of phase.

__Free Boundary Problems and Applications, Pitman,Edited by Fremond, Damlamian and Bossavit__. 1984; 1-14.E. DiBenedetto and R.E. Showalter. Free Boundary Problems for a Degenerate Parabolic System.

__Journal of Differential Equations__. 1983; 1((50)): 1-19.E.DiBenedetto. Continuity of Weak Solutions to a General Porous Medium Equation.

__Indiana Univ. Math. Jour__. 1983; 1((32)): 83.E. DiBenedetto and R. Spigler. An Algorithm for the One Phase Stefan Problem.

__Rendiconti Seminario Matematico Univ. Padova__. 1983; ((69)): 109-34.J.R. Cannon E. DiBenedetto and K.G. Knightly. The Bidimensional Stefan Problem with Convection: The Time Dependent Case.

__Comm. in Part. Diff. Eqs__. 1983; 14((8)): 1549-604.E.DiBenedetto. Local Regularity of Weak Solutions of Degenerate Elliptic Equations.

__Non Linear Analysis TMA__. 1983; 8((7)): 827-50.E.DiBenedetto. Change of Phase with Convection.

__Applied Nonlinear Functional Analysis,Peter Lang, Edited by R. Gorenflo and K.H. Hoffmann__. 1983; 25: 1-18.E.DiBenedetto. Continuity of Weak Solutions to Certain Singular Parabolic Equations.

__Annali di Matematica Pura ed Applicata__. 1982; IV((CXXX)): 131-77.E.DiBenedetto and R.E. Showalter. A Pseudo-Parabolic Variational Inequality and Stefan Problem.

__Non Linear Analysis TMA__. 1982; 6: 279-99.E. DiBenedetto. Continuity for Singular Parabolic Equations.

__Nonlinear Phenomena in Mathematical Sciences, Acad. Press__. 1982; (()): 307-12.E.DiBenedetto. Continuity for Singular Parabolic Equations.

__Nonlinear Phenomena in Mathematical Sciences, Acad. Press, Edited by Laksmikantam__. 1982; 307-12.E. DiBenedetto and M. Pierre. On the Maximum Principle for Pseudo-Parabolic Equations.

__Indiana Univ. Math. Jour__. 1981; 30(()): 821-54.E. DiBenedetto. Interior and Boundary Regularity for a Class of Free Boundary Problems.

__Pitman 78, ; Edited by A.Fasano and M. Primicerio__. 1981; 78: 383-95.E. DiBenedetto and R.E. Showalter. Implicit Degenerate Evolution Equations and Applications.

__SIAM Jour. Math. Anal__. 1981; 12((5)): 731-51.J.R. Cannon , E.DiBenedetto and G.K. Knightly. The Steady State Stefan Problem with Convection.

__Archive for Rational Mechanics and Analalysis__. 1980; 73(()): 79-97.J.R. Cannon and E.DiBenedetto. On the Existence of Weak Solutions to an n-dimensional Stefan Problem with Nonlinear Boundary Conditions.

__SIAM Jour. Math. Anal__. 1980; 4((11)): 632-45.E. DiBenedetto. Regularity Results for the two Phase N-dimensional Stefan Problem.

__Boll. Un. Mat. Ital__. 1980; 1: 129-52.E.DiBenedetto. The Initial Value Problem for the Boussinesq Equations with Data in Lp.

__Approximation Methods for Navier Stokes Equations, Springer Lecture Notes__. 1979; 771(()): 129-44.J.R. Cannon and E.DiBenedetto. The Steady State Stefan Problem with Convection with Mixed Temperature and Nonlinear Boundary Conditions.

__Proceedings of Free Boundary Problems Symposium, Pavia__. 1979; (()): 232-65.G. Borgioli and M. Ughi and E.DiBenedetto. Stefan Problems with Nonlinear Boundary Conditions: The Polygonal Method.

__ZAMM__. 1978; 58: 530-46.J.R. Cannon and E.DiBenedetto. On the Existence of Solutions of Boundary Value Problems in Fast Chemical Reactions.

__Boll. Un. Mat. Ital__. 1978; 15((5)): 835-43.D. Andreucci, G. Caruso and E.DiBenedetto. Ill-Posed Hele-Shaw Flows.

__Free Boundary Problems, ISNM, Birkhauser__. 147(()): 27-52. Available Postdoctoral Position Details

**Posted: 10/20/2004**

The Biomathematics Study Group at Vanderbilt invites applications for non tenure track positions, beginning in the Fall of 2005. Each position is a two-year appointment at the level of post-doctoral fellow or research assistant professor depending on qualifications of the applicant and may carry teaching duties.

Successful applicants will participate in collaborative research with the members of the Biomathematics Study Group as well as scientists in life sciences and medicine at Vanderbilt,

Topics include, but are not limited to, neuroscience, molecular biology and signal transduction, ligand-receptor binding problems, cellular kinetics, functional registration and imaging, growth of malignant tissues, computational biology and physiology and the mathematical modeling of medical procedures and devices.

The applicants must have a doctorate in mathematics or a closely related area (e.g., computer science or physics) and a background in biology or medicine.

Applictions and supporting material should be sent as a single mailing to:

Biomathematics Study Group

Department of Mathematics

Vanderbilt University

1326 Stevenson Center

Nashville, TN 37240

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