Quenching Phenomenon of Solutions for Parabolic Equations with Singular Absorption on Graphs

Abstract

In this paper, we study the quenching phenomenon of solutions for parabolic equations with singular absorption under the mixed boundary conditions on graphs. Firstly, we prove the local existence of solutions via Schauder fixed point theorem. Then, under certain conditions we obtain the estimates of quenching time and quenching rate. Finally, numerical experiments are shown to explain the theoretical results.