Emmanuele DiBenedetto, Ph.D.

Professor

em.diben@vanderbilt.edu

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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., Università degli Studi di Firenze, Florence
Office Address
1416 Stevenson Center
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 ). 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. Poincaré. 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. Poincaré. 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
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 Please include an e-mail address, fax number and a research summary. Please do not send additional information (e.g., letters of recommendation) unless requested to do so.