Initial boundary value problem for a class of wave equations of Hartree type

被引：2
作者：
Zhang, Hongwei [1 ]
Su, Xiao [1 ]
机构：
[1] Henan Univ Technol, Dept Math, Zhengzhou 450001, Peoples R China
来源：
STUDIES IN APPLIED MATHEMATICS | 2022年 / 149卷 / 03期
基金：
中国国家自然科学基金;
关键词：
blowup; global existence; Hartree-type nonlinearity; wave-Hartree equation; GLOBAL WELL-POSEDNESS; KLEIN-GORDON EQUATION; BLOW-UP PHENOMENON; SCATTERING-THEORY; PLATE EQUATION; EXISTENCE; INSTABILITY; THRESHOLD; NONEXISTENCE;
D O I：
10.1111/sapm.12521
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider a class of wave equations of Hartree type on a bounded smooth convex domain with Dirichlet boundary condition. By applying the standard semigroup theory, we get the local existence result. Using potential well theory, we derive the condition of global existence of weak solutions. With the help of potential well theory and convexity method, we give blowup results for solutions when the initial energy is nonnegative or negative.
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页码：798 / 814
页数：17
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