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.

引用

页码：798 / 814

页数：17

共 50 条

[1] Global existence and blowup of solutions to a class of wave equations with Hartree type nonlinearity
Zhang, Hongwei
Su, Xiao
Liu, Shuo
NONLINEARITY, 2024, 37 (06)
[2] Initial value problem for a class of fourth-order nonlinear wave equations
Chen, Guo-wang
Hou, Chang-shun
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2009, 30 (03) : 391 - 401
[3] Initial boundary value problem for a class of p-Laplacian equations with logarithmic nonlinearity
Zeng, Fugeng
Huang, Yao
Shi, Peng
MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2021, 18 (04) : 3957 - 3976
[4] Initial boundary value problem for a damped wave equation with logarithmic nonlinearity
Li, Haixia
QUAESTIONES MATHEMATICAE, 2023, 46 (05) : 993 - 1008
[5] Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity
Di, Huafei
Shang, Yadong
Song, Zefang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2020, 51
[6] Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations
Bilgin, Bilgesu A.
Kalantarov, Varga K.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 403 (01) : 89 - 94
[7] Initial boundary value problems for nonlinear dispersive wave equations
Escher, Joachim
Yin, Zhaoyang
JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 256 (02) : 479 - 508
[8] Initial boundary value problem for a Kirchhoff wave model with strong nonlinear damping
Ding, Hang
Zhou, Jun
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (14) : 14794 - 14813
[9] INITIAL BOUNDARY VALUE PROBLEM OF A CLASS OF MIXED PSEUDO-PARABOLIC KIRCHHOFF EQUATIONS
Cao, Yang
Zhao, Qiuting
ELECTRONIC RESEARCH ARCHIVE, 2021, 29 (06): : 3833 - 3851
[10] Initial boundary value problem for a class of fourth-order wave equation with viscous damping term
Xu, Runzhang
Wang, Shuo
Yang, Yanbing
Ding, Yunhua
APPLICABLE ANALYSIS, 2013, 92 (07) : 1403 - 1416

← 1 2 3 4 5 →