Null-exact controllability of a semilinear cascade system of parabolic-hyperbolic equations

This paper is concerned with the null-exact controllability of a cascade system formed by a semilinear heat and a semilinear wave equation in a cylinder Ω×(0, T). More precisely, we intend to drive the solution of the heat equation (resp. the wave equation) exactly to zero (resp. exactly to a prescr...

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Detalles Bibliográficos
Autores: Fernández Cara, Enrique, González Burgos, Manuel, Teresa de Oteyza, María de la Luz de
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2006
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/46196
Acceso en línea:http://hdl.handle.net/11441/46196
https://doi.org/10.3934/cpaa.2006.5.639
Access Level:acceso abierto
Palabra clave:Semilinear systems
Parabolic-hyperbolic equations
Controllability
Observability inequalities
Descripción
Sumario:This paper is concerned with the null-exact controllability of a cascade system formed by a semilinear heat and a semilinear wave equation in a cylinder Ω×(0, T). More precisely, we intend to drive the solution of the heat equation (resp. the wave equation) exactly to zero (resp. exactly to a prescribed but arbitrary final state). The control acts only on the heat equation and is supported by a set of the form ω × (0, T), where ω ⊂ Ω. In the wave equation, the restriction of the solution to the heat equation to another set O × (0, T) appears. The nonlinear terms are assumed to be globally Lipschitz-continuous. In the main result in this paper, we show that, under appropriate assumptions on T, ω and O, the equations are simultaneously controllable.