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.
Kokocki, Effect of resonance on the existence of periodic solutions for strongly damped wave equation,Nonlinear Analysis125, 167–200 (2015)
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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.