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arXiv · 2512.21321

Large time behavior of the solution to the Cauchy problem for the discrete p-Laplacian with density on infinite graphs

Alan A. Tedeev
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Abstract

We consider the Cauchy problem for the nonstationary discrete p-Laplacian with inhomogeneous density \r{ho}(x) on an infinite graph which supports the Sobolev inequality. For nonnegative solutions when p > 2, we prove the precise rate of stabilization in time, provided \r{ho}(x) is a non-power function. When p > 2 and \r{ho}(x) goes to zero fast enough, we prove the universal bound. Our technique relies on suitable energy inequalities and a new embedding result.

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Alan A. Tedeev. 2025-12-24. Large time behavior of the solution to the Cauchy problem for the discrete p-Laplacian with density on infinite graphs. https://arxiv.org/abs/2512.21321

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