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...
| Authors: | , , |
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2006 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/46196 |
| Online Access: | http://hdl.handle.net/11441/46196 https://doi.org/10.3934/cpaa.2006.5.639 |
| Access Level: | Open access |
| Keyword: | Semilinear systems Parabolic-hyperbolic equations Controllability Observability inequalities |
| Summary: | 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. |
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