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On the Solutions of a Porous Medium Equation with Exponent Variable

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  • Huashui Zhan

Abstract

The paper studies the initial-boundary value problem of a porous medium equation with exponent variable. How to deal with nonlinear term with the exponent variable is the main dedication of this paper. The existence of the weak solution is proved by the monotone convergent method. Moreover, according to the different boundary value conditions, the stability of weak solutions is studied. In some special cases, the stability of weak solutions can be proved without any boundary value condition.

Suggested Citation

  • Huashui Zhan, 2019. "On the Solutions of a Porous Medium Equation with Exponent Variable," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-15, August.
    • Handle: RePEc:hin:jnddns:9290582
    DOI: 10.1155/2019/9290582
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