ON THE BEHAVIOR OF SOLUTIONS FOR A SYSTEM OF MULTIDIMENSIONAL HEAT TRANSFER EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS
Rakhmonov Z.R
Urolov G’.B
Abstract
Consider the following nonlinear system of parabolic equations coupled via
nonlinear boundary conditions
References
References
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. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov, Blow-
up in Quasilinear Parabolic Equations, Walter de Gruyter, Berlin, 1995.
A.S.Kalashnikov, Some problems of the qualitative theory of nonlinear degenerate
parabolic equations of second order, Russian Math. Surveys, 42, (1987), 169-222.
E. Dibenedetto, Degenerate Parabolic Equations, Springer-Verlag, Berlin, New
York, 1993.
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.
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.
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.
Chen Botao, Mi Yongsheng, Mu Chunlai. Global existence and nonexistence for a
doubly degenerate parabolic system coupled via nonlinear boundary flux. Acta
Mathematica Scientia, 31B(2), 2011, 681-693.
Zhou J, Mu C L, Critical curve for a non-Newtonian polytropic filtration system
coupled via nonlinear boundary flux. Nonlinear Anal, 2008, 68: 1-11.