Existence and asymptotic stability for a semilinear damped wave equation with dynamic boundary conditions involving variable nonlinearity

Saf Salim, Touil Nadji, Abita Rahmoune

Abstract


We study the solvability of a class of quasilinear elliptic equations with \((p(x),k(x))\)-growth structure and with nonlinear boundary conditions in the context of Kelvin-Voigt damping with arbitrary data. We approach our problem in a suitable functional classes by considering the so-called Lebesgue and Sobolev spaces with variable exponents. In the first step we establish existence and uniqueness results of solutions for the considered model if the data are regular enough. Our main idea is essentially based on using fixed point theory and Faedo-Galerkin approaches and includes some new techniques. Second, we assume the data is large enough and show that the energy grows exponentially.

Keywords


Viscoelastic equation, Global Existence, Nonlinear Dissipation, Energy estimates

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2025.1.06

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