Existence and uniqueness of renormalized solutions to nonlinear multivalued parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent
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Abstract
In this paper, we prove the existence and the uniqueness of renormalized solution to a nonlinear multivalued parabolic problem β(u)t - div a(x,∇ u) ∋ f , with homogeneous Dirichlet boundary conditions and L1-data. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. Some a-priori estimates are used to obtain our results.
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Kyelem, B. A., Zongo, A. O., & Zongo, F. (2022). Existence and uniqueness of renormalized solutions to nonlinear multivalued parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent. Gulf Journal of Mathematics, 12(1), 41-55. https://doi.org/10.56947/gjom.v12i1.778
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