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Volume 35, Issue 2
Blowup Behavior of Solutions to an $\omega$-Diffusion Equation on the Graph

Liping Zhu & Lin Huang

DOI: 10.4208/jpde.v35.n2.3

J. Part. Diff. Eq., 35 (2022), pp. 148-162.

Published online: 2022-04

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  • 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.

  • Keywords

Simple graph, discrete, blowup time, blowup rate.

  • AMS Subject Headings

35B40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

791558012@qq.com (Liping Zhu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-35-148, author = {Zhu , Liping and Huang , Lin}, title = {Blowup Behavior of Solutions to an $\omega$-Diffusion Equation on the Graph}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {2}, pages = {148--162}, 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n2.3}, url = {http://global-sci.org/intro/article_detail/jpde/20448.html} }
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 -

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.

Zhu , Liping and Huang , Lin. (2022). Blowup Behavior of Solutions to an $\omega$-Diffusion Equation on the Graph. Journal of Partial Differential Equations. 35 (2). 148-162. doi:10.4208/jpde.v35.n2.3
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