Existence and uniqueness of bounded strong solutions to the inverse problem for a semilinear strongly damped wave equation with almost periodic data is established by reducing to a direct problem and extending solutions from finite intervals to the whole real line.
Lions,Quelques methodes de resolution des problemes aux limites non lineares, Dunod, Paris, Gauthieir-Villars
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An Inverse Almost Periodic Problem for a Semilinear Strongly Damped Wave Equation
Existence and uniqueness of bounded strong solutions to the inverse problem for a semilinear strongly damped wave equation with almost periodic data is established by reducing to a direct problem and extending solutions from finite intervals to the whole real line.