Abstract
The Dirichlet problem for the degenerate and singular parabolic p(x)-Laplace equation with one spatial variable is considered. We prove the existence of the unique weak solution such that the derivatives u t and u x of a solution u belong to \({L_{\infty}}\). Moreover for the singular case we prove the existence of the strong solution i.e. such that u t , u x and u xx belong to \({L_{\infty}}\).
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Tersenov, A.S. The one dimensional parabolic p(x)-Laplace equation. Nonlinear Differ. Equ. Appl. 23, 27 (2016). https://doi.org/10.1007/s00030-016-0377-y
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DOI: https://doi.org/10.1007/s00030-016-0377-y