[1]黄骏.一类非线性抛物型方程整体解的存在性与衰减估计[J].东南大学学报(自然科学版),2001,31(6):103-107.[doi:10.3969/j.issn.1001-0505.2001.06.025] 　Huang Jun.Existence and Decaying Estimation of Global Solutions for a Nonlinear Parabolic Equation[J].Journal of Southeast University (Natural Science Edition),2001,31(6):103-107.[doi:10.3969/j.issn.1001-0505.2001.06.025] 点击复制 一类非线性抛物型方程整体解的存在性与衰减估计() 分享到： var jiathis_config = { data_track_clickback: true };

31

2001年第6期

103-107

2001-11-20

文章信息/Info

Title:
Existence and Decaying Estimation of Global Solutions for a Nonlinear Parabolic Equation

Author(s):
Huang Jun
Department of Applied Mathematics, Southeast University, Nanjing 210096, China)

Keywords:

O175.26
DOI:
10.3969/j.issn.1001-0505.2001.06.025

Abstract:
The nonlinear function f(x,t,u,u) contains an unknown function u and its gradient u and a known function φ(x,t). Using the methods of regularization and prior-estimation, the author proves the existence of global solution of a nonlinear parabolic equation as long as the nonlinear function f(x,t,u,u) satisfies the conditions of structure and smoothing and the initial value function is small. Decaying estimation is obtained.

参考文献/References:

[1] Tsutsumi M.Existence and nonexistence of global solutions for nonlinear parabolic equations.Publ RIMS Kyoto Univ,1972—1973,8:211～229
[2] Nakao M.A difference inequality and its application to nonlinear evolution equations.J Math Soc Japan,1978,30(4):747～762
[3] Nakao M.Lp-estimation of solutions of some nonlinear degenerate diffusion equations.J Math Soc Japan,1985,37(1):41～63
[4] Nakao M.Global solutions for some nonlinear parabolic equations with nonmonotonic perturbations.Nonlinear Anal,1986,10(3):299～314
[5] Zhao Junning.Existence and nonexistence of solutions for ut=div(|u|p-2u)+f(u,u,x,t).J Math Anal Appl,1993,172(1):130～146
[6] Ladyenskaja O A,Solonnikov V A,Ural′ceva N N.Linear and quasi-linear equations of parabolic type.Rhode Island:Amer Math Soc,1968.72～73
[7] Alikakos N D.Lp bounds of solutions of reaction-diffusion equations.Comm Part Diff Eq,1979,4(8):827～868
[8] Gu Yonggeng,Luo Peizhu,Ding Xiaxi.Generalized soultions of strongly non-linear parabolic equations.Scientica Sinca Series A,1983,XXVI(11):1129～1143

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