Non-resonance for a strongly dissipative wave equation in higher dimensions |
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Authors: | Alain Haraux |
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Institution: | (1) Analyse Numérique, T. 55-65, 5ème étage, Université Pierre et Marie Curie, 4, place Jussieu, 75230 Paris Cedex 05, France |
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Abstract: | Under some regularity conditions, a non-resonance property is established for a semi-linear forced wave equation with a strong local damping term and Dirichlet boundary conditions in a bounded open domain. In dimension less than or equal to six, the damping term can grow at infinity like an arbitrarily large power of the velocity. If a viscosity term is added, in dimension less or equal to four a stronger result is obtained, and this property allows to construct almost periodic solutions for an arbitrary forcing term in a suitable regularity class. |
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