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.
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页数：10
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