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Uniqueness results and asymptotic behavior of solutions with boundary blow-up for logistic-type porous media equations

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Abstract

Under the proper structure conditions on the nonlinear term f(u) and weight function b(x), the paper shows the uniqueness and asymptotic behavior near the boundary of boundary blow-up solutions to the porous media equations of logistic type −Δu = a(x)u 1/m − b(x)f(u) with m > 1.

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Authors and Affiliations

  1. Department of Mathematics, Nantong University, 226007, Nantong, People’s Republic of China

    Yujuan Chen

  2. Science Research Center, Harbin Institute of Technology, 150080, Harbin, People’s Republic of China

    Mingxin Wang

Authors
  1. Yujuan Chen
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  2. Mingxin Wang
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Correspondence to Yujuan Chen.

Additional information

Y. Chen was partially supported by the foundation of Jiangsu Education Commission 07KJD110166, Jiangsu Planned Projects for Postdoctoral Research Funds 0702004C and the project in Nantong University 06Z011, 08B02. M. Wang was supported by NSFC Grant 10771032.

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Chen, Y., Wang, M. Uniqueness results and asymptotic behavior of solutions with boundary blow-up for logistic-type porous media equations. Z. Angew. Math. Phys. 61, 277–292 (2010). https://doi.org/10.1007/s00033-009-0015-1

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  • DOI: https://doi.org/10.1007/s00033-009-0015-1

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