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.