TY - JOUR
T1 - Blowup Behavior of Solutions to an $\omega$-Diffusion Equation on the Graph
AU - Zhu , Liping
AU - Huang , Lin
JO - Journal of Partial Differential Equations
VL - 2
SP - 148
EP - 162
PY - 2022
DA - 2022/04
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n2.3
UR - https://global-sci.org/intro/article_detail/jpde/20448.html
KW - Simple graph, discrete, blowup time, blowup rate.
AB - <p style="text-align: justify;">In this article, we discuss the blowup phenomenon of solutions to the&nbsp; $\omega$-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.</p>