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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...