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Large time behavior of solutions to Newtonian filtration equation with nonlinear boundary sources

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Abstract.

This paper deals with the exterior problem of the Newtonian filtration equation with nonlinear boundary sources. The large time behavior of solutions including the critical Fujita exponent are determined or estimated. An interesting phenomenon is illustrated that there exists a threshold value for the coefficient of the lower order term, which depends on the spacial dimension. Exactly speaking, the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this threshold.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China

    Zejia Wang & Hang Gao

  2. Department of Mathematics, Jilin University, Changchun, 130012, P. R. China

    Zejia Wang, Jingxue Yin & Chunpeng Wang

Authors
  1. Zejia Wang
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  2. Jingxue Yin
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  3. Chunpeng Wang
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  4. Hang Gao
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Corresponding author

Correspondence to Zejia Wang.

Additional information

Supported by the NNSF of China and the China Postdoctoral Science Foundation.

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Wang, Z., Yin, J., Wang, C. et al. Large time behavior of solutions to Newtonian filtration equation with nonlinear boundary sources. J. evol. equ. 7, 615–648 (2007). https://doi.org/10.1007/s00028-007-0324-9

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  • DOI: https://doi.org/10.1007/s00028-007-0324-9

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