Título:
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Asymptotics for some nonlinear damped wave equation: finite time convergence versus exponential decay results
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Autores:
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Díaz Díaz, Jesús Ildefonso ;
Baji, B. ;
Cabot, Alexandre
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Tipo de documento:
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texto impreso
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Editorial:
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Elsevier (Gauthier-Villars), 2007-11
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/restrictedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Ecuaciones diferenciales
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Tipo = Artículo
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Resumen:
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Given a bounded open set Omega subset of R-n and a continuous convex function Phi: L-2(Omega) -> R, let us consider the following damped wave equation u(tt) - Delta u + partial derivative Phi(u(t)) 0, (t, x) is an element of (0, +infinity) x Omega, (S) under Dirichlet boundary conditions. The notation partial derivative Phi refers to the subdifferential of Phi in the sense of convex analysis. The nonlinear term partial derivative Phi allows to modelize a large variety of friction problems. Among them, the case Phi = vertical bar.vertical bar L-1 corresponds to a Coulomb friction, equal to the opposite of the velocity sign. After we have proved the existence and uniqueness of a solution to (S), our main purpose is to study the asymptotic properties of the dynamical system (S). In two significant situations, we bring to light an interesting phenomenon of dichotomy: either the solution converges in a finite time or the speed of convergence is exponential as t -> +infinity. We also give conditions which ensure the finite time stabilization of (S) toward some stationary solution.
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En línea:
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https://eprints.ucm.es/id/eprint/15287/2/35.pdf
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