A variational approach to a shape design problem for the wave equation |
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| Authors: | Arnaud Münch Pablo Pedregal Francisco Periago |
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| Affiliation: | 1. Laboratoire de mathématiques, Université de Franche-Comté, UMR CNRS 6623, 25030 Besançon, France;2. Departamento de Matemáticas, ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain;3. Departamento de Matemática Aplicada y Estadística, ETSI Industriales, Universidad Politécnica, 30203 Cartagena, Spain |
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| Abstract: | The problem of determining the optimal damping set for the stabilization of the wave equation may be not well-posed. By means of a vector variational reformulation and use of gradient Young measures, we present a general methodology to relax this kind of problems. From the optimal Young measure associated with the relaxed problem, we obtain information concerning minimizing sequences for the original problem as well as continuity properties of the relaxed cost function. To cite this article: A. Münch et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). |
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