Upper and lower bounds for the blow-up time in quasilinear reaction diffusion problems

Juntang Ding; Xuhui Shen

doi:10.3934/dcdsb.2018135

Article Contents

2018, Volume 23, Issue 10: 4243-4254. Doi: 10.3934/dcdsb.2018135

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Upper and lower bounds for the blow-up time in quasilinear reaction diffusion problems

Juntang Ding^, and
Xuhui Shen

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China

* Corresponding author: Juntang Ding
* Corresponding author: Juntang Ding

Received: August 31, 2017

Early access: April 2018

Published: September 2018

This work was supported by the National Natural Science Foundation of China (No. 61473180).

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Abstract

In this paper, we consider a quasilinear reaction diffusion equation with Neumann boundary conditions in a bounded domain. Basing on Sobolev inequality and differential inequality technique, we obtain upper and lower bounds for the blow-up time of the solution. An example is also given to illustrate the abstract results obtained of this paper.

Keywords:

Quasilinear reaction diffusion equation,
upper bound,
lower bound.

Mathematics Subject Classification: 35k55, 35k60.

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References

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