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

Abstract: 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.