Chen G.-Q., Di Benedetto E. (editors) Nonlinear Partial Differential Equations

1999. 303 pages.
ISBN-10: 0821811967 ISBN-13: 978-0821811962This volume is a collection of refereed original research papers and expository articles and stems from the scientific program of the 1997-98 Nonlinear PDE Emphasis Year at Northwestern University, which was jointly sponsored by Northwestern University and the National Science Foundation. Most of the papers presented are from the distinguished mathematicians who spoke at the International Conference on Nonlinear Partial Differential Equations, March 21-24, 1998, Evanston, IL.
The book is a cross-section of the most significant recent advances and current trends and directions in nonlinear partial differential equations and related topics. Contributions range from modern approaches to the classical theory in elliptic and parabolic equations to nonlinear hyperbolic systems of conservation laws and their numerical treatment.
The general guiding idea in editing this volume has been twofold. On one hand, we have solicited the papers that contribute in a substantial way to the general analytical treatment of the theory of nonlinear partial differential equations. On the other hand, we have attempted to collect the contributions to computational methods and applications, originating from significant realistic mathematical models of natural phenomena, to seek synergistic links between theory and modeling and computation and to underscore current research trends in partial differential equations. The borderline between these two aspects of mathematical research is rather fuzzy. We have also selected a set of papers that would bridge them.