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Authors: ABITA RAHMOUNE.
Received 25 November 2021; Accepted 02 March 2023.
pp. 425-443
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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.
Keywords: Viscoelastic equation, Global Existence, Nonlinear Dissipation, Energy estimates.
