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Finite extinction time for subsolutions of the weighted Leibenson equation on Riemannian manifolds [PDF]

arXiv
We consider on Riemannian manifolds the non-linear evolution equation $$\rho \partial _{t}u=\Delta _{p}u^{q}.$$ Assuming that the manifold satisfies a weighted Sobolev inequality and under certain assumptions on $p, q$ and function $\rho$, we prove that weak subsolutions to this equation have finite extinction time.
arxiv