Translator Disclaimer
April, 2018 Blow-up Phenomena for a Porous Medium Equation with Time-dependent Coefficients and Inner Absorption Term Under Nonlinear Boundary Flux
Suping Xiao, Zhong Bo Fang
Taiwanese J. Math. 22(2): 349-369 (April, 2018). DOI: 10.11650/tjm/170802

Abstract

This paper deals with blow-up phenomena for an initial boundary value problem of a porous medium equation with time-dependent coefficients and inner absorption term in a bounded star-shaped region under nonlinear boundary flux. Using the auxiliary function method and modified differential inequality technique, we establish some conditions on time-dependent coefficient and nonlinear functions to guarantee that the solution $u(x,t)$ exists globally or blows up at some finite time $t^{\ast}$. Moreover, the upper and lower bounds for $t^{\ast}$ are derived in the higher dimensional space. Finally, some examples are presented to illustrate applications of our results.

Citation

Download Citation

Suping Xiao. Zhong Bo Fang. "Blow-up Phenomena for a Porous Medium Equation with Time-dependent Coefficients and Inner Absorption Term Under Nonlinear Boundary Flux." Taiwanese J. Math. 22 (2) 349 - 369, April, 2018. https://doi.org/10.11650/tjm/170802

Information

Received: 22 December 2016; Revised: 29 April 2017; Accepted: 1 August 2017; Published: April, 2018
First available in Project Euclid: 8 September 2017

zbMATH: 06965375
MathSciNet: MR3780722
Digital Object Identifier: 10.11650/tjm/170802

Subjects:
Primary: 35B30, 35B40, 35K65

Rights: Copyright © 2018 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.22 • No. 2 • April, 2018
Back to Top