Об асимптотике решений системы нелинейных уравнений диффузии с нелинейными краевыми условиями
Ключевые слова:
нелинейная параболическая система, диффузия, критические индексы типа Фуджиты, разрушение, асимптотика.Аннотация
В данной работе мы изучаем асимптотическое поведение автомодельных решений нелинейныхпараболические уравнениясистема, связанная с нелокальными краевыми условиями. Построены различные автомодельные решения задачи кросс-диффузии для случая медленной диффузии, являющиеся асимптотиками решений рассматриваемой задачи. Получен главный член асимптотики автомодельных решений.
Библиографические ссылки
Wu, Z.Q., Zhao, J.N., Yin, J.X. and Li, H.L., Nonlinear Diffusion Equations, Singapore: World Scientific, 2001.
M. Aripov, Standard Equation's Methods for Solutions to Nonlinear Problems, FAN, Tashkent, 1988.
A.S.Kalashnikov, Some problems of the qualitative theory of nonlinear degenerate parabolic equations of second order, Russian Math. Surveys, 42, (1987), 169-222.
Levine, H., The role of critical exponents in blowup theorems, SIAM Rev., 32(2), 1990, 262-288.
F. Quiros and J. D. Rossi. Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions, Indiana Univ. Math. J. 50, no. 1, 2001, 629-654.
Zheng, S.N., Song, X.F. and Jiang, Z.X., Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl., 298(1), 2004, 308-324.
Xiang, Zhaoyin Mu, Chunlai. Blowup behaviors for degenerate parabolic equations coupled via nonlinear boundary flux. Commun. Pure Appl. Anal., vol. 6, no. 2, 2007, 487–503.
Cui, Z.J., Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Analysis: Theory, Methods and Applications, 68(10), 2008, 3201-3208.
Li Z.P., Cui Z.J. and Mu C.L., Critical curves for fast diffusive polytropic filtration equations coupled through boundary, Appl. Anal., 87(9), 2008, 1041-1052.
Li Z.P. and Mu C.L., Critical curves for fast diffusive non-Newtonian equations coupled via nonlinear boundary flux, J. Math. Anal. Appl., 340(2), 2008, 876-883.
Wang Zejia, Zhou Qian, Lou Wenqi. Critical exponents for porous medium systems coupled via nonlinear boundary flux. Nonlinear Anal. 71, no. 5-6, 2009, 2134–2140.
Zhaoyin Xiang, Chunlai Mu and Yulan Wang. Critical curve of the non-Newtonian polytropic filtration equations coupled via nonlinear boundary flux. Rocky Mountain Journal of Mathematics, vol. 39, no. 2, 2009, 689-705.
Zhaoyin Xiang. Global existence and nonexistence for diffusive polytropic filtration equations with nonlinear boundary conditions. Z. Angew. Math. Phys., vol. 61, Issue 3, 2010, pp 467-478.
Yongsheng Mi, Chunlai Mu, Botao Chen, A nonlinear diffusion system coupled via nonlinear boundary flux, Journal of Mathematical Analysis and Applications, Volume 376, Issue 2, 15 April 2011, Pages 613-624
Xu and Song. Critical parameter equations for degenerate parabolic equations coupled via nonlinear boundary flux. Boundary Value Problems, 2011:15, 2011, 1-13.
Mi, Y.S., Mu, C.L., and Chen, B.T., Critical exponents for a nonlinear degenerate parabolic system coupled via nonlinear boundary flux, J. Korean Math. Soc., 48(3), 2011, 513-527.
Yong-Sheng Mi, Chunlai Mu, and Deng-Ming Liu. Global existence and blow-up for a doubly degenerate parabolic equation system with nonlinear boundary conditions. Glasgow Math. J. 54, 2012, 309–324.
Mi Yongsheng, Mu Chunlai. Global existence and blow-up of solutions to a class of doubly degenerate parabolic equations coupled via nonlinear boundary flux. Advances in Mathematics (China), Vol.43, No.3, 2014, 398-410.
Wanjuan Du and Zhongping Li. Critical exponents for heat conduction equation with a nonlinear Boundary condition. Int. Jour. of Math. Anal. vol. 7, 11, 2013, 517-524
