Harnack inequality for porous medium equations with a blow-up term along the Finsler-geometric flow

Abstract

We prove global gradient estimates for positive bounded solutions of porous medium equations with a blow-up term $$\partial_{t}u=\Delta_{m}u^{p}+cu^{q}$$ on a compact $n$-dimensional Finsler manifold $(M^{n},F(t),m)$ evolving under the Finsler-geometric flow. Then, we obtain Harnack type inequalities.