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 estimatesAbstract
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.
Mathematics Subject Classification (2010): 74D10, 74G25, 74G30, 40E10, 35B45.
Received 25 November 2021; Accepted 02 March 2023
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