Philipp Sürig

Conservation of mass for solutions of Leibenson's equation on Riemannian Manifolds

We consider on a Riemannian manifold $M$ the Leibenson equation \begin{equation*}\label{eqabs}\partial _{t}u=\Delta _{p}u^{q},\end{equation*} where $p>1$ and $q>0$. When $q(p-1)\geq 1$, we prove conservation of mass for solutions of Leibenson's equation assuming only the volume bound $V(x_0, r)\leq \exp\left(C r^{\frac...