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This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. Among the themes explored in this volume are the following: the increasing role of dynamical systems theory in understanding partial differential equations; the central importance of certain prototypical equations, such as the complex Ginzburg-Landau, nonlinear Schrodinger, and Korteweg-de Vries equations; and problems in fluid mechanics and the limits of physically motivated heuristic theories of fluids.
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