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An evolution equation involving the normalized $P$-Laplacian

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  • This paper considers an initial-boundary value problem for the evolution equation associated with the normalized $p$-Laplacian. There exists a unique viscosity solution $u,$ which is globally Lipschitz continuous with respect to $t$ and locally with respect to $x.$ Moreover, we study the long time behavior of the viscosity solution $u$ and compute numerical solutions of the problem.
    Mathematics Subject Classification: Primary: 35K92, 35K61, 35K65, 35Q91; Secondary: 65M06.


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