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This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirichlet boundary conditions. We obtain the conditions for global and blow-up solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or blow-up, but also whether the blowing up occurs for any positive initial data or just for large ones. Moreover, we establish the precise blow-up rate.
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참고문헌 (27)
참고문헌 신청
J. R. Anderson / 1991 / Local existence and uniqueness of solutions of degenerate parabolic equations / Comm. Partial Differential Equations 16(1):105~143
J. R. Anderson / 1997 / Global existence for degenerate parabolic equations with a nonlocal forcing / Math. Methods Appl. Sci 20(13):1069~1087
D. G. Aronson / 1982 / Stabilization of solutions of a degenerate nonlinear diffusion problem / Nonlinear Anal 6(10):1001~1022
D. E. Carlson / 1972 / Linear Thermoelasticity, Encyclopedia, Vol. Via/2 / Springer
Y. P. Chen / 2004 / Blow-up for a porous medium equation with a localized source / Appl. Math. Comput 159(1):79~93
J. R. Anderson / 1997 / Global existence for degenerate parabolic equations with a nonlocal forcing / Math. Methods Appl. Sci 20(13):1069~1087
D. G. Aronson / 1982 / Stabilization of solutions of a degenerate nonlinear diffusion problem / Nonlinear Anal 6(10):1001~1022
D. E. Carlson / 1972 / Linear Thermoelasticity, Encyclopedia, Vol. Via/2 / Springer
Y. P. Chen / 2004 / Blow-up for a porous medium equation with a localized source / Appl. Math. Comput 159(1):79~93
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