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Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions

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  • Huimin Tian
  • Lingling Zhang

Abstract

In this paper, we devote to studying the blow-up phenomena for a porous medium equation under nonlocal boundary conditions. Based on auxiliary functions and differential inequality technique, we derive the sufficient conditions to guarantee the existence of blow-up solutions under different measures and obtain an upper bound for blow-up time. Moreover, we demonstrate the lower bounds for blow-up time under some appropriate measures in and in the higher-dimensional space , respectively. At last, two examples are given to illustrate the applications of main results.

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  • Huimin Tian & Lingling Zhang, 2020. "Blow-Up Solution of a Porous Medium Equation with Nonlocal Boundary Conditions," Complexity, Hindawi, vol. 2020, pages 1-20, June.
    • Handle: RePEc:hin:complx:9037287
    DOI: 10.1155/2020/9037287
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