Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations

被引：0

作者：

Di, Huafei ^{[1
]}

Song, Zefang ^{[2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[2] Guangzhou Univ, Sch Econ & Stat, Guangzhou 510006, Peoples R China

来源：

ADVANCES IN MATHEMATICAL PHYSICS | 2021年 / 2021卷

关键词：

CAHN-HILLIARD EQUATION; 4TH-ORDER WAVE-EQUATION; GLOBAL EXISTENCE; BEHAVIOR;

D O I：

10.1155/2021/6668355

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations u(t) - beta u(xx) - ku(xxt) + gamma u(xxxx)( )= f (u(x))(x). At low initial energy level (J(u(0)) < d), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approximation and potential well methods but also obtain the finite time blow-up result by adopting the potential well and improved concavity skills. Finally, we also discussed the finite time blow-up phenomenon for certain solutions of these problems with high initial energy.

引用

页数：10

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