Constantine Michael Dafermos
Constantine Michael Dafermos
Alumni-Alumnae University Professor Emeritus of Applied Mathematics
Overview
I received a Diploma in Civil Engineering from the National Technical University of Athens (1964) and a Ph.D. in Mechanics from the Johns Hopkins University (1967). I have served as Assistant Professor at Cornell University (1968-1971),and as Associate Professor (1971-1975) and Professor (1975-) in the Division of Applied Mathematics at Brown University. Since 1984, I have been the Alumni-Alumnae University Professor at Brown.
Brown Affiliations
Research Areas
continuum mechanics | gas dynamics | hyperbolic conservation laws | nonlinear elasticity | nonlinear partial differential equations
Publications
| Dafermos, Constantine. "Hyperbolic balance laws with relaxation." Discrete and Continuous Dynamical Systems, vol. 36, no. 8, 2016, pp. 4271-4285. |
| Dafermos, Constantine M. "Asymptotic behavior of BV solutions to hyperbolic systems of balance laws with relaxation." J. Hyper. Differential Equations, vol. 12, no. 02, 2015, pp. 277-292. |
| Dafermos, Constantine M. "Periodic BV solutions of hyperbolic balance laws with dissipative source." Journal of Mathematical Analysis and Applications, vol. 428, no. 1, 2015, pp. 405-413. |
| Dafermos, Constantine M. "BV Solutions of Hyperbolic Balance Laws with Relaxation in the Absence of Conserved Quantities." SIAM Journal on Mathematical Analysis, vol. 46, no. 6, 2014, pp. 4014-4034. |
| Dafermos, Constantine M. "Asymptotic behavior of BV solutions to the equations of nonlinear viscoelasticity." Communications in Information and Systems, vol. 13, no. 2, 2013, pp. 201-209. |
| Dafermos, Constantine M. "BV solutions for hyperbolic systems of balance laws with relaxation." Journal of Differential Equations, vol. 255, no. 8, 2013, pp. 2521-2533. |
| Dafermos, Constantine. "Heat Flow with Shocks in Media with Memory." Indiana Univ. Math. J., vol. 62, no. 5, 2013, pp. 1443-1456. |
| DAFERMOS, CONSTANTINE M. "HYPERBOLIC SYSTEMS OF BALANCE LAWS WITH WEAK DISSIPATION II." J. Hyper. Differential Equations, vol. 10, no. 01, 2013, pp. 173-179. |
| Dafermos, Constantine M. "Long Time Behavior of Periodic Solutions to Scalar Conservation Laws in Several Space Dimensions." SIAM Journal on Mathematical Analysis, vol. 45, no. 4, 2013, pp. 2064-2070. |
| Dafermos, C. M. "Non-convex entropies for conservation laws with involutions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 371, no. 2005, 2013, pp. 20120344-20120344. |
| Dafermos, Constantine M. "Redistribution of Damping in Viscoelasticity." Communications in Partial Differential Equations, vol. 38, no. 7, 2013, pp. 1274-1286. |
| Dafermos, C.M. "Maximal dissipation in equations of evolution." Journal of Differential Equations, vol. 252, no. 1, 2012, pp. 567-587. |
| DAFERMOS, CONSTANTINE M. "N-WAVES IN HYPERBOLIC BALANCE LAWS." J. Hyper. Differential Equations, vol. 09, no. 02, 2012, pp. 339-354. |
| DAFERMOS, CONSTANTINE M. "GENERALIZED CHARACTERISTICS AND THE HUNTER–SAXTON EQUATION." J. Hyper. Differential Equations, vol. 08, no. 01, 2011, pp. 159-168. |
| SHEARER, MICHAEL, DAFERMOS, CONSTANTINE. "FINITE TIME EMERGENCE OF A SHOCK WAVE FOR SCALAR CONSERVATION LAWS." J. Hyper. Differential Equations, vol. 07, no. 01, 2010, pp. 107-116. |
| Dafermos, Constantine M., Pan, Ronghua. "Global $BV$ Solutions for the P -System with Frictional Damping." SIAM Journal on Mathematical Analysis, vol. 41, no. 3, 2009, pp. 1190-1205. |
| Dafermos, Constantine M. "Strong shocks in nonisentropic gas dynamics." Acta Mathematica Scientia, vol. 29, no. 4, 2009, pp. 973-979. |
| Dafermos, Constantine. "A variational approach to the Riemann problem for hyperbolic conservation laws." Discrete and Continuous Dynamical Systems, vol. 23, no. 1/2, 2008, pp. 185-195. |
| Dafermos, Constantine, Kröner, Dietmar, LeVeque, Randall. "Hyperbolic Conservation Laws." Oberwolfach Rep., 2008, pp. 3139-3200. |
| Dafermos, Constantine M. "Wave fans are special." Acta Math. Appl. Sin. Engl. Ser., vol. 24, no. 3, 2008, pp. 369-374. |
| Chen, Gui-Qiang, Dafermos, Constantine M., Slemrod, Marshall, Wang, Dehua. "On Two-Dimensional Sonic-Subsonic Flow." Commun. Math. Phys., vol. 271, no. 3, 2007, pp. 635-647. |
| Dafermos, Constantine M. "Continuous solutions for balance laws." Ricerche mat., vol. 55, no. 1, 2006, pp. 79-92. |
| DAFERMOS, C. M. "HYPERBOLIC SYSTEMS OF BALANCE LAWS WITH WEAK DISSIPATION." J. Hyper. Differential Equations, vol. 03, no. 03, 2006, pp. 505-527. |
| Dafermos, Constantine, Kröner, Dietmar, LeVeque, Randall. "Hyperbolic Conservation Laws." Oberwolfach Rep., 2004, pp. 915-962. |
| Cheverry, C., Dafermos, C.M, Glimm, J. "The modulation equations of nonlinear geometric optics." Communications in Partial Differential Equations, vol. 21, no. 7-8, 1996, pp. 1119-1140. |
Research
Research Overview
I work on the interface between continuum mechanics and the theory of partial differential equations. In recent years, my research has focused on nonlinear hyperbolic systems of conservation laws, whose solutions spontaneously develop singularities that propagate as shock waves. I am interested in the interplay between thermodynamics and analysis, in the theory of these systems, and have been striving to elucidate the fundamental role of entropy, as a stabilizing agent.
Research Statement
Over the past three years, I have been involved in the following research projects:
(1) Uniqueness and stability of solutions to hyperbolic systems of conservative laws, arising in elastodynamics and electromagnetism, which are endowed with involutions, a polyconvex entropy and a set of contingent entropies.
(2) Continuous solutions of hyperbolic balance laws with applications to the Hunter-Saxton equation.
(3) Irrotational sonic-subsonic gas flow via the method of compensated compactness.
(1) Uniqueness and stability of solutions to hyperbolic systems of conservative laws, arising in elastodynamics and electromagnetism, which are endowed with involutions, a polyconvex entropy and a set of contingent entropies.
(2) Continuous solutions of hyperbolic balance laws with applications to the Hunter-Saxton equation.
(3) Irrotational sonic-subsonic gas flow via the method of compensated compactness.
Funded Research
NSF Grant # DMS-020288 (Hyperbolic Conservation Laws in Continuum Physics)
NSF Grant # DMS-0244295 (FRG Collaborative Research: Multi-Dimensional Problems for the Euler Equations)
NSF Grant # DMS-0244295 (FRG Collaborative Research: Multi-Dimensional Problems for the Euler Equations)
Background
Education and Training
| Year | Degree | Institution |
|---|---|---|
| 1967 | PhD | The Johns Hopkins University |
| 1964 | BA | National Technical University of Athens |
Honors and Awards
Fellow American Academy of Arts and Sciences, 2001-.
Correspondent Member, Academy of Athens, 1988-.
Honorary Professor, Academia Sinica, China, 2004-.
Foreign Member, Accademia Nazionale dei Lincei, Roma 2011-.
Member, Board of Governors, Weizmann Institute of Science (Israel), 1995-.
Fellow, SIAM, 2009-.
Fellow, AMS 2013-.
Fellow, Society of Scholars, Johns Hopkins University.
Chairman, Society for Natural Philosophy, 1977-78.
Secretary, International Society for the Interaction of Mathematics and Mechanics, 1984-86.
Ordway Chair, University of Minnesota, 1985.
Keeley Fellowship, Wadham College, Oxford, 2001.
Honorary Doctorate, University of Athens, 1987.
Honorary Doctorate, National Technical University (Greece), 1991.
Honorary Doctorate, University of Crete, 2001.
SIAM W.T. and Idalia Reid Prize, 2000.
Cataldo e Angiola Agostinelli Prize, 2011.
GALILEO Medal, City of Padua, 2012.
ISIMM Prize, 2014.
AMS Norbert Weiner Prize, 2016.
Elected to the National Academy of Sciences, 2016.
Affiliations
Affiliations
Editorial Board of following publications:
Quarterly of Applied Mathematics, Associate Managing Editor
Acta Mathematica Scientia, Chief Co-Editor
Annali di Matematica Pura ed Applicata
Archive for Rational Mechanics and Analysis
Mathematics Applied in Science and Technology
Communications in Applied Analysis
Proceedings of the Royal Society of Edinburgh
Ricerche di Matematica
Revista Matematica Complutense
Bulletin of Greek Mathematical Society
Journal of Dynamics and Differential Equations
Journal of Hyperbolic Differential Equations
Member, Board of Governors and Scientific and Academic Advisory Committee, Weizmann Institute of Science, Israel
Member, National Committee on Research and Technology, Greece
Member, Advisory Board, Institute of Mathematics, Academy of Sciences, Czech Republic
Member, Scientific Advisory Board, Archimedes Center, Crete, Greece
Member, Scientific Advisory Panel, IRIMA, University of Wales, U.K.
Member, Institute of Numerical Analysis, Crete, Greece
Member, Scientific Committee, XIV International Conference on Nonlinear Hyperbolic PDE, Padova, Italy
Member, Scientific Committee, Workshop, Crete, Greece
Cochairman, Scientific Committee, International Conference in memory of Guoping Li, Wuhan, China
Member, Scientific Committee, EUROCONFERENCES, Crete
Member, Scientific Committee, WASCOM 2011
Member, Scientific Committee, International Conference on Conservation Laws, Tata Institute, Bangalore, India
Member, Jury for habilitation thesis, Université Pierre et Marie Curie, Paris.
Member, Promotion Committee, University of Crete, Greece
Quarterly of Applied Mathematics, Associate Managing Editor
Acta Mathematica Scientia, Chief Co-Editor
Annali di Matematica Pura ed Applicata
Archive for Rational Mechanics and Analysis
Mathematics Applied in Science and Technology
Communications in Applied Analysis
Proceedings of the Royal Society of Edinburgh
Ricerche di Matematica
Revista Matematica Complutense
Bulletin of Greek Mathematical Society
Journal of Dynamics and Differential Equations
Journal of Hyperbolic Differential Equations
Member, Board of Governors and Scientific and Academic Advisory Committee, Weizmann Institute of Science, Israel
Member, National Committee on Research and Technology, Greece
Member, Advisory Board, Institute of Mathematics, Academy of Sciences, Czech Republic
Member, Scientific Advisory Board, Archimedes Center, Crete, Greece
Member, Scientific Advisory Panel, IRIMA, University of Wales, U.K.
Member, Institute of Numerical Analysis, Crete, Greece
Member, Scientific Committee, XIV International Conference on Nonlinear Hyperbolic PDE, Padova, Italy
Member, Scientific Committee, Workshop, Crete, Greece
Cochairman, Scientific Committee, International Conference in memory of Guoping Li, Wuhan, China
Member, Scientific Committee, EUROCONFERENCES, Crete
Member, Scientific Committee, WASCOM 2011
Member, Scientific Committee, International Conference on Conservation Laws, Tata Institute, Bangalore, India
Member, Jury for habilitation thesis, Université Pierre et Marie Curie, Paris.
Member, Promotion Committee, University of Crete, Greece
Teaching
Teaching
| APMA 0200 - Introduction to Modelling |
| APMA 0330 - Methods of Applied Mathematics I, II |
| APMA 0350 - Applied Ordinary Differential Equations |
| APMA 1930T - Waves |
| APMA 2120 - Hilbert Spaces and Their Applications |
| APMA 2230 - Partial Differential Equations |
| APMA 2230 - Partial Differential Equations I |
| APMA 2240 - Partial Differential Equations |