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Asymptotic non-stability and blow-up at boundary for solutions of a filtration equation

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Abstract

For a class of nonlinear filtration equation with nonlinear second-third boundary value condition, it is shown that a priori boundary of the solution can be estimated and controlled by initial data and integral on the boundary of the region. The priori estimate of the solutions was established by iterative method. By using this estimate the solutions may blow-up on the boundary of the region and thus it may have asymptotic non-stability.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Xiamen University, Xiamen, 361005, P. R. China

    Zhen-chao Cao (Professor)

  2. Department of Mathematics, China Institute of Metrology, Hangzhou, 310018, P. R. China

    Peng-nian Chen

Authors
  1. Zhen-chao Cao
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  2. Peng-nian Chen
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Corresponding author

Correspondence to Zhen-chao Cao.

Additional information

Communicated by ZHANG Hong-qing

Project supported by the National Natural Science Foundation of China (Nos. 60274008 and 10171084)

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Cao, Zc., Chen, Pn. Asymptotic non-stability and blow-up at boundary for solutions of a filtration equation. Appl. Math. Mech.-Engl. Ed. 26, 1643–1648 (2005). https://doi.org/10.1007/BF03246274

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  • DOI: https://doi.org/10.1007/BF03246274

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