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Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources

Critical Exponents for Fast Diffusion Equations with Nonlinear Boundary Sources
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摘要 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_o and the critical Fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case. 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_o and the critical Fujita exponent q_c for the problem considered,and show that q_o=q_c for the multidimensional Non-Newtonian polytropic filtration equation with nonlinear boundary sources,which is quite different from the known results that q_o〈q_c for the onedimensional case;moreover,the value is different from the slow case.
作者 WANG LU-SHENG WANG ZE-JIA
机构地区 School of Mathematics
出处 《Communications in Mathematical Research》 CSCD 2011年第2期97-104,共8页 数学研究通讯（英文版）
基金 The Fundamental Research Funds for the Central Universities and the NSF(11071100) of China
关键词 exterior domain critical global exponent critical Fujita exponent fast diffusion equation exterior domain, critical global exponent, critical Fujita exponent, fast diffusion equation
分类号 O175.2 [理学—基础数学] O175.26 [理学—基础数学]
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参考文献20

  • 1DiBenedetto, E., Degenerate Parabolic Equations, Springer, New York, 1993.
  • 2Wu, Z. Q., Zhao, J. N., Yin, J. X. and Li, H. L., Nonlinear Diffusion Equations, World Scientific Publishing Co., Inc., River Edge, N J, 2001.
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  • 7Pang, Peter Y. H., Sun, F. Q. and Wang, M. X., Existence and non-existence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55(2006), 1113-1134.
  • 8Pang, Peter Y. H., Wang, Z. J. and Yin, J. X., Critical exponents for nonlinear diffusion equations with nonlinear boundary sources, J. Math. Anal. Appl., 343(2008), 654-662.
  • 9Quir6s, F. and Rossi, J. D., Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions, Indiana Univ. Math. J., 50(2001), 629-654.
  • 10Wang, Z. J., Yin, J. X. and Wang, C. P., Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition, Appl. Math. Lett., 20(2007), 142-147.
Communications in Mathematical Research
2011年 第2期

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