Nonlinear Differential Equations

Thierry Cazenave

ISBN 10: 3764371498 / ISBN 13: 9783764371494

Editore: Springer, Basel, Birkhäuser Basel Nov 2005, 2005

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This item is printed on demand - it takes 3-4 days longer - Neuware -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 ×(0,+ ) tt u=0 on ×(0,+ ) 0 (1. 1) u+g(u)=0 on ×(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 ×(0,+ ) tt 0 u=0 on ×(0,+ ) 0 (1. 2) u = g(u ) f (u)on ×(0,+ ) t 1 1 0 1 u(x,0) = u (x); u (x,0) = u (x),x , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s 0, that is, f represents, for i i i each i, an attractive force. 518 pp. Englisch. Codice articolo 9783764371494

Dati bibliografici

Titolo: Nonlinear Differential Equations

Casa editrice: Springer, Basel, Birkhäuser Basel Nov 2005

Data di pubblicazione: 2005

Legatura: Buch

Condizione: Neu

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Riassunto:

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 ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(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? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.

Dalla quarta di copertina:

This volume represents a broad survey of current research in the fields of nonlinear analysis and nonlinear differential equations. It is dedicated to Djairo G. de Figueiredo on the occasion of his 70^th birthday. The collection of 34 research and survey articles reflects the wide range of interests of Djairo de Figueiredo, including:
- various types of nonlinear partial differential equations and systems, in particular equations of elliptic, parabolic, hyperbolic and mixed type;
- equations of Schrödinger, Maxwell, Navier-Stokes, Bernoulli-Euler, Seiberg-Witten, Caffarelli-Kohn-Nirenberg;
- existence, uniqueness and multiplicity of solutions;
- critical Sobolev growth and connected phenomena;
- qualitative properties, regularity and shape of solutions;
- inequalities, a-priori estimates and asymptotic behavior;
- various applications to models such as asymptotic membranes, nonlinear plates and inhomogeneous fluids.
The contributions of so many distinguished mathematicians to this volume document the importance and lasting influence of the mathematical research of Djairo de Figueiredo. The book thus is a source of new ideas and results and should appeal to graduate students and mathematicians interested in nonlinear problems.