Global existence and uniqueness for viscoelastic equations with nonstandard growth conditions
DOI:
https://doi.org/10.24193/subbmath.2024.2.12Keywords:
Viscoelastic equation, Global Existence, Nonlinear Dissipation, Energy estimates.Abstract
This paper is devoted to the study of generalized viscoelastic nonlinear equations with Dirichlet-Neumann boundary conditions. We establish the local and uniqueness of weak solutions results in Sobolev spaces with variable exponents. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space.
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