# Constantine Michael Dafermos Alumni-Alumnae University Professor of Applied Mathematics

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

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## Research

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)