Global Existence and Blow-Up of Solutions for a Porous Medium Equation-Reference-Cited by-同舟云学术

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Global Existence and Blow-Up of Solutions for a Porous Medium Equation

Published:2012-02 Issue: Volume:461 Page:532-536
ISSN:1662-8985
Container-title:Advanced Materials Research
language:
Short-container-title:AMR

Author:

Gao Yun Zhu¹,Meng Xi¹,Gai Hong¹

Affiliation:

1. Beihua University

Abstract

In this paper, a porous medium equation with local source and nonlocal boundary condition is studied. By using the fixed point theorem and comparison principle. The global existence and blow-up of solutions are obtained .

Publisher

Trans Tech Publications, Ltd.

Subject

General Engineering

Link

https://www.scientific.net/AMR.461.532.pdf

Reference8 articles.

1. J. R. Anderson, Local existence and uniqueness of solutions of degenerate parabolic equations, Commun. Partial. Differential Equations 16, 105-143 (1991).

2. Y. P. Chen, Q. Liu, H. J. Gao, Boundedness of global solutions of a porous medium equation with a localized source, Nonlinear Anal. 64, 2168-2182(2006).

3. W. A. Day, Extensions of propertity of heat equation to linear thermoelasticity and other theories, Quart. Appl. Math. 40, 319-330 (1982).

4. K. Deng, H. A. Levien, The role of critical exponents in blow-up theorems: The sequel, J. Math. Anal. Appl. 243, 85-126 (2000).

5. J. I. Diaz, R. Kerser, On a non-linear degenerate parabolic equation in infiltration or evaporation through a porous medium, J. Differ. Equat. 238(1987), 368-403.

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