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Volume 27, Issue 2
Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources

Lusheng Wang & Zejia Wang

Commun. Math. Res., 27 (2011), pp. 97-104.

Published online: 2021-05

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  • Abstract

In this paper, we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent $q_0$ and the critical Fujita exponent $q_c$ for the problem considered, and show that $q_0 = q_c$ for the multi-dimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that $q_0 < q_c$ for the one-dimensional case; moreover, the value is different from the slow case.

  • Keywords

exterior domain, critical global exponent, critical Fujita exponent, fast diffusion equation.

  • AMS Subject Headings

35K55, 35B33

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-97, author = {Wang , Lusheng and Wang , Zejia}, title = {Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {2}, pages = {97--104}, abstract = {

In this paper, we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent $q_0$ and the critical Fujita exponent $q_c$ for the problem considered, and show that $q_0 = q_c$ for the multi-dimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that $q_0 < q_c$ for the one-dimensional case; moreover, the value is different from the slow case.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19092.html} }
TY - JOUR T1 - Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources AU - Wang , Lusheng AU - Wang , Zejia JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 104 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19092.html KW - exterior domain, critical global exponent, critical Fujita exponent, fast diffusion equation. AB -

In this paper, we study the large time behavior of solutions to a class of fast diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent $q_0$ and the critical Fujita exponent $q_c$ for the problem considered, and show that $q_0 = q_c$ for the multi-dimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources, which is quite different from the known results that $q_0 < q_c$ for the one-dimensional case; moreover, the value is different from the slow case.

Wang , Lusheng and Wang , Zejia. (2021). Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources. Communications in Mathematical Research . 27 (2). 97-104. doi:
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