一类含非局部源的退化抛物型方程整体解的存在性
GLOBAL EXISTENCE FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS WITH NON-LOCAL SOURCE
摘要
本文研究了一类含非局部源的退化非线性抛物型方程的解的整体存在性和有限时刻爆破性质.
出处
《南京大学学报(数学半年刊)》
CAS
2002年第1期31-36,共6页
Journal of Nanjing University(Mathematical Biquarterly)
参考文献11
-
1Diaz J I and Kersner R. On a Nonlinear Degenerate Parabolic Equation in Infiltration or Evaporation Through a Porous Medium, Journal of Differential Equations, 1987,69: 368-403.
-
2Galaktionov V G. Boundary Values Problems for the Nonlinear Parabolic Equation ut =Au +1+up, Differential Equations, 1981, 71:836-842.
-
3Cantrell R S and Cosner C. Diffusive Logistic Equations with Indefinite Weights: Population Mod els in Disrupted Environments Ⅱ, SIAM J. Math. Anal. ,1991,22: 1043-1064.
-
4Aronson D G, Crandall M G and Peletier L A. Stabilization of Solutions of a Degenerate Nonlinear Diffusion Problem, J. Nonlinear Anal. Theory Method Appl., 1982, 6: 1001-1022.
-
5Anderson J R. Local Existence and Uniqueness of Solutions of Degenerate Parabolic Equations, Comm. Partial Diiferential Equations, 1991, 16 : 105- 143.
-
6Anderson J R and Deng K. Global Existencefor Degenerate Parabolic Equations with a Non-Local Forcing, Math. Meth. Appl. Sci., 1997,20: 1069-1087.
-
7Furter J and Grinfeld M. Local vs. Non-Local Interactions in Population Dynamics, J. Math. Bi- ology, 1989,27: 65-80.
-
8Deng W B, Duan Z W and Xie C H. The Blow-up Ratefor a Degenerate Parabolic Equation with a Non-Local Source, J. Math. Anal. Appl., 2001, 264(2): 577-597.
-
9Wang M and Wang Y. Properties ofPositive Solutionsfor Non-Local Reaction-Diffusion Prob lems, Math. Meth. Appl. Sci., 1996, 19: 1141-1156.
-
10Pao C V. Blowing-up ofSolutionfor a Non-Local Reaction-Diffusion Problem in Combustion Theory, J. Math. Anal. Appl., 1992,16: 591-600.