Exact thresholds for global existence to the nonlinear beam equations with and without a damping

被引：1

作者：

Yuan, Yiyin ^{[1
]}

Tian, Shuai ^{[1
]}

Qing, Jun ^{[2
]}

Zhu, Shihui ^{[1
]}

机构：

[1] Sichuan Normal Univ, Sch Math Sci & VC, VR Key Lab, Chengdu 610066, Peoples R China

[2] Guangzhou Railway Polytech, Dept Fundamental Educ, Guangzhou 510430, Peoples R China

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2023年 / 64卷 / 01期

关键词：

4TH-ORDER WAVE-EQUATIONS; STRAIN; NONEXISTENCE; SCATTERING;

D O I：

10.1063/5.0103472

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the Cauchy problem for focusing nonlinear beam equations with and without a damping term. By constructing two pairs of invariant flows, we obtain the exact thresholds for the global existence and blow-up to the above equations in the sense that both thresholds are explicitly expressed by the L-2-norm of the fourth-order nonlinear elliptic equation without any damping.

引用

页数：17

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