Inverse problem for semilinear wave equation with strong damping

Abstract

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The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using an additional integral type overdetermination condition.

Keywords

• semilinear wave equation
• inverse coefficient problem
• existence of solutions
• initial-boundary value problem
• strong damping