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The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.

This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It considers important examples, including the heat, Klein-Gordon, and Schroodinger equations, placing each in the analytical framework which allows the most striking statement of the key properties. With the exceptions of the treatment of the Schroodinger equation, the book employs the most standard methods, each developed in enough generality to cover other cases. This new edition includes a chapter on...

This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u u =-u- u in ? x(0, +?) ? tt ? ? ? ? u=0 on ? x(0, +?) 0 (1. 1) ? ? u+g(u)=0 on ? x(0, +?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x), x? ?, t n where ? is a bounded domain of R, n? 1, with a smooth boundary ? = ? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u u =?f (u)in? x(0, +?) ? tt 0 ? ? ? ? u=0 on ? x(0, +?) 0 (1. 2) ? ? u =?g(u...