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Trend to spatial homogeneity for solutions to semilinear damped wave equations

Published online by Cambridge University Press:  14 November 2011

J. Solà-Morales  and
M. València
J. Solà-Morales
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), Spain
M. València
Affiliation:
Departament de Matemàtiques, ETSEIB, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
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Synopsis

The semilinear damped wave equations

subject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 117 - 126
Copyright
Copyright © Royal Society of Edinburgh 1987

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