Blow-Up Phenomena for a Class of Generalized Double Dispersion Equations

被引：5

作者：

Di, Huafei ^{[1
,2
]}

Shang, Yadong ^{[1
,2
]}

机构：

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

[2] Guangzhou Univ, Guangdong Higher Educ Inst, Key Lab Math & Interdisciplinary Sci, Guangzhou 510006, Guangdong, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2019年 / 39卷 / 02期

关键词：

double dispersion; blow up; upper bound; lower bound; 35L35; 31A35; 35B44; NONLINEAR-WAVE EQUATIONS; BOUNDARY VALUE-PROBLEMS; ASYMPTOTIC-BEHAVIOR; CAUCHY-PROBLEM; GLOBAL EXISTENCE;

D O I：

10.1007/s10473-019-0219-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study the blow-up phenomena of generalized double dispersion equations u(tt) - u(xx) - u(xxt) + u(xxxx) - u(xxtt) = f(u(x))(x). Under suitable conditions on the initial data, we first establish a blow-up result for the solutions with arbitrary high initial energy, and give some upper bounds for blow-up time T* depending on sign and size of initial energy E(0). Furthermore, a lower bound for blow-up time T* is determined by means of a differential inequality argument when blow-up occurs.

引用

页码：567 / 579

页数：13

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