ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (3): 249-261.

ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

王卫东^1,2, 张全德^1,2

1. Department of Mathematics, Shaanxi Normal University, Shaanxi 710062. China;
2. College of Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:1996-05-10 修回日期:1996-10-14 出版日期:1998-09-25 发布日期:1998-09-25
基金资助:
This work is supported by NSF

ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

Wang Weidong^1,2, Zhang Quande^1,2

1. Department of Mathematics, Shaanxi Normal University, Shaanxi 710062. China;
2. College of Xi'an Jiaotong University, Xi'an 710049, China

Received:1996-05-10 Revised:1996-10-14 Online:1998-09-25 Published:1998-09-25
Supported by:
This work is supported by NSF

摘要/Abstract

摘要： This paper gives the sufficient and necessary conditions of existence of global solutions and decay estimates of the solutions for the initial boundary value problem of some nonlinear parabolic equations with small initial energy and the nonlinear power less than Sobolev critical value. The existence, nonexistence and the decay estimates of global solutions are considered. The conditions that initial energy is small and nonlinear power is less than Sobolev critical value is imposed.

关键词: nonlinear parabolic equation, initial boundary value problem, global solution

Abstract: This paper gives the sufficient and necessary conditions of existence of global solutions and decay estimates of the solutions for the initial boundary value problem of some nonlinear parabolic equations with small initial energy and the nonlinear power less than Sobolev critical value. The existence, nonexistence and the decay estimates of global solutions are considered. The conditions that initial energy is small and nonlinear power is less than Sobolev critical value is imposed.

Key words: nonlinear parabolic equation, initial boundary value problem, global solution

王卫东, 张全德. ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS[J]. 数学物理学报(英文版), 1998, 18(3): 249-261.

Wang Weidong, Zhang Quande. ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS[J]. Acta mathematica scientia,Series B, 1998, 18(3): 249-261.

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ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

ON GLOBAL EXISTENCE AND NONEXISTENCE FOR SOME NONLINEAR PARABOLIC EQUATIONS

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