Blowup Behavior of Solutions to an $\omega$-Diffusion Equation on the Graph

Abstract

In this article, we discuss the blowup phenomenon of solutions to the  $\omega$-diffusion equation with Dirichlet boundary conditions on the graph. Through Banach fixed point theorem, comparison principle, construction of auxiliary function and other methods, we prove the local existence of solutions, and under appropriate conditions the blowup time and blowup rate estimation are given. Finally, numerical experiments are given to illustrate the blowup behavior of the solution.