Nonlinear Semigroups, Partial Differential Equations and Attractors: Proceedings of a Symposium Held in Washington, D.C., August 3-7, 1987 (Lecture Notes in Mathematics)

The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It soon became clear, however, that the dynamical systems approach interfaced significantly with many important branches of applied mathematics. As a consequence, the scope of this resulting proceedings volume is an enlarged one with coverage of a wider range of research topics. There are many problems in the natural sciences which are naturally formulated in terms of nonlinear partial differential equations. Over the years, new methods and special techniques have evolved for the study of nonlinear problems. In addition, there has been a great deal of recent activity devoted to the study of stochastic solutions to nonlinear differential equations in cases where the conventional wisdom'' physics leads us to believe that only deterministic solutions exist. Many of these studies have been numerical and confined to either maps or ordinary differential equations, which are more easily analyzed than are partial differential equations. Recently however, various methods have been developed for the study of partial differential equations which, because of the complicated nature of these equations, are a valued addition to the mathematical sciences. A general method that has been very effective in the treatment of large classes of nonlinear partial differential equations makes use of the theory of nonlinear semigroups. Given appropriate conditions, these semigroups generate solutions to nonlinear evolution equations which may have a compact global attractor with finite Hausdorff dimension. This type of analysis to numerous nonlinear partial differential equations. Most of the papers contained in the present collection are concerned with nonlinear semigroups State-space formulation for functional differential equations of neutral-type....Pages 1-10 Some remarks on forced integrable systems....Pages 11-17 Some remarks on the nonlinear Schrödinger equation in the critical case....Pages 18-29 On the integrability of nonlinear evolution equations....Pages 30-43 On quasilinear hyperbolic integrodifferential equations in unbounded domains....Pages 44-55 Positive solutions for semilinear elliptic systems....Pages 56-67 Recent rigorous results in Thomas-Fermi theory....Pages 68-82 Methods of computing fractal dimensions....Pages 83-95 Asymptotic behavior of solutions to quasimonotone parabolic systems....Pages 96-116 Global existence for semilinear parabolic systems via Lyapunov type methods....Pages 117-121 A difference inclusion....Pages 122-130 Spectrum estimations for the generalized quantum Henon-Heiles system....Pages 131-135 A survey of local existence theories for abstract nonlinear initial value problems....Pages 136-184 The transient semiconductor problem with generation terms, II....Pages 185-198 Switching systems and periodicity....Pages 199-210 Breathers for the Sine-Gordon equation....Pages 211-217 The riccati equation revisited....Pages 218-233 T.l. Gill, W.w. Zachary (eds.). Proceedings Of The Second Symposium On Nonlinear Semigroups, Partial Differential Equations, And Attractors, Held At Howard University--pref. Includes Bibliographical References.