Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents
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U. Traoré
urbain.traore@yahoo.fr
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DOI:
https://doi.org/10.4067/S0719-06462021000300385Abstract
In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in \(L^1\). By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.
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