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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Haraux, A. Non-resonance for a strongly dissipative wave equation in higher dimensions. Manuscripta Math 53, 145–166 (1985). https://doi.org/10.1007/BF01174015
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DOI: https://doi.org/10.1007/BF01174015