论文信息 - Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition

Critical exponents of the non-Newtonian polytropic filtration equation with nonlinear boundary condition

This work is concerned with the critical exponent of the non-Newtonian polytropic filtration equation with nonlinear boundary conditions. We obtain the critical global existence exponent and critical Fujita exponent by constructing various self-similar supersolutions and subsolutions.

[1] H. Fujita. On the blowing up of solutions fo the Cauchy problem for u_t=Δu+u^ , 1966 .

[2] Howard A. Levine,et al. The Role of Critical Exponents in Blowup Theorems , 1990, SIAM Rev..

[3] Keng Deng,et al. The Role of Critical Exponents in Blow-Up Theorems: The Sequel , 2000 .

[4] Zhuoqun Wu,et al. Nonlinear Diffusion Equations , 2002 .

[5] On Critical Exponents for the Heat Equation with a Mixed Nonlinear Dirichlet–Neumann Boundary Condition , 1997 .

[6] A. S. Kalashnikov. Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations , 1987 .

[7] Howard A. Levine,et al. On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary , 1996 .

[8] J. McLeod. Nonlinear Diffusion Equations. , 1985 .

[9] On critical exponents for the heat equation with a nonlinear boundary condition , 1996 .

[10] C. Pao. The cauchy problem of a degenerate parabolic equation , 1977 .

[11] Keng Deng,et al. ON CRITICAL EXPONENTS FOR A SYSTEM OF HEAT EQUATIONS COUPLED IN THE BOUNDARY CONDITIONS , 1994 .