[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]
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一类非线性抛物型方程整体解的存在性与衰减估计()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
31
期数:
2001年第6期
页码:
103-107
栏目:
数学、物理学、力学
出版日期:
2001-11-20

文章信息/Info

Title:
Existence and Decaying Estimation of Global Solutions for a Nonlinear Parabolic Equation
作者:
黄骏
东南大学应用数学系,南京 210096
Author(s):
Huang Jun
Department of Applied Mathematics, Southeast University, Nanjing 210096, China)
关键词:
广义解 非线性 抛物型 存在性 衰减估计
Keywords:
generalized solution nonlinear parabolic existence of solution decaying estimation
分类号:
O175.26
DOI:
10.3969/j.issn.1001-0505.2001.06.025
摘要:
在非线性函数f(x,t,u,u)同时含有未知函数u与它的梯度u,以及x,t的某个已知函数φ(x,t)的情形下,运用正则化和先验估计的方法得到结论:只要函数f(x,t,u,u)满足结构性条件和某些光滑性条件,初值函数u0(x)适当小,非线性抛物型方程的初边值问题的整体解必定存在,且给出了解的衰减估计.
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:

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[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
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备注/Memo

备注/Memo:
作者简介:黄骏,男,1954年生,副教授.
更新日期/Last Update: 2001-11-20