Hyperbolic Conservation Laws in Continuum Physics

Professor Dafermos 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). He has served as Assistant Professor at Cornell University (1968-1971),and as Associate Professor (1971-1975) and Professor (1975- present) in the Division of Applied Mathematics at Brown University. In addition, Professor Dafermos has served as Director of the Lefschetz Center of Dynamical Systems (1988-1993, 2006-2007), as Chairman of the Society for Natural Philosophy (1977-1978) and as Secretary of the International Society for the Interaction of Mathematics and Mechanics. Since 1984, he has been the Alumni-Alumnae University Professor at Brown.In addition to several honorary degrees, he has received the SIAM W.T. and Idalia Reid Prize (2000), the Cataldo e Angiola Agostinelli Prize of the Accademia Nazionale dei Lincei (2011), the Galileo Medal of the City of Padua (2012), and the Prize of the International Society for the Interaction of Mechanics and Mathematics (2014). He was elected a Fellow of SIAM (2009) and a Fellow of the AMS (2013). In 2016 he received the Wiener Prize, awarded jointly by the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM).

• I Balance Laws. - II Introduction to Continuum Physics. - III Hyperbolic Systems of Balance Laws. - IV The Cauchy Problem. - V Entropy and the Stability of Classical Solutions. - VI The L1 Theory for Scalar Conservation Laws. - VII Hyperbolic Systems of Balance Laws in One-Space Dimension. - VIII Admissible Shocks. - IX Admissible Wave Fans and the Riemann Problem. - X Generalized Characteristics. -  XI Scalar Conservation Laws in One Space Dimension. - XII Genuinely Nonlinear Systems of Two Conservation Laws. - XIII The Random Choice Method. - XIV The Front Tracking Method and Standard Riemann Semigroups. - XV Construction of BV Solutions by the Vanishing Viscosity Method. - XVI BV Solutions for Systems of Balance Laws. - XVII Compensated Compactness. - XVIII Steady and Self-similar Solutions in Multi-Space Dimensions. - Bibliography. - Author Index. - Subject Index.

“This book is a contribution to the fields of mathematical analysis and partial differential equations and their broad interactions with various branches of applied mathematics and continuum physics, whose value cannot be overstated. … a useful resource for a variety of courses as well as an almost encyclopedic reference point for advanced researchers. … It is a great achievement that will influence the PDEs and mathematical analysis community for years to come.” (Marta Lewicka, Mathematical Reviews, November, 2017)