Decay of Mass of the Solution to the Cauchy Problem of the p-Laplacian with Absorption on Infinite Graphs
Abstract
We consider the Cauchy problem for the nonstationary discrete p-Laplacian with inhomogeneous density 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 ho(x) is a non-power function. When p > 2 and 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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