Asymptotic behavior and finite time blow up for damped fourth order nonlinear evolution equation-Reference-Cited by-同舟云学术

Asymptotic behavior and finite time blow up for damped fourth order nonlinear evolution equation

Published:2021-04-07 Issue:3-4 Volume:122 Page:349-369
ISSN:1875-8576
Container-title:Asymptotic Analysis
language:
Short-container-title:ASY

Author:

Han Jiangbo¹,Xu Runzhang¹,Yang Yanbing¹

Affiliation:

1. College of Mathematical Sciences, Harbin Engineering University, 150001, People’s Republic of China. E-mails: han1825141364@163.com, xurunzh@163.com, xurunzh@hrbeu.edu.cn, yangyanbheu@163.com, yangyanbing@hrbeu.edu.cn

Abstract

This paper investigates the initial boundary value problem for a class of fourth order nonlinear damped wave equations modeling longitudinal motion of an elasto-plastic bar. By applying a suitable potential well-convexity method, we derive the global existence, asymptotic behavior and finite time blow up for the considered problem with more generalized nonlinear functions at subcritical initial energy level. Further for arbitrarily positive initial energy we give some sufficient conditions ensuring finite time blow up.

Publisher

IOS Press

Subject

General Mathematics

Reference29 articles.

1. The effect of microstructure on elastic-plastic models;An;SIAM J. Appl. Math.,1994

2. A weakly nonlinear analysis of elasto-plastic-microstructure models;An;SIAM J. Appl. Math.,1995

3. Initial boundary value problem for a class of semi-linear pseudo-parabolic equations with logarithmic nonlinearity;Chen;J. Differential Equations,2015

4. Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity;Chen;Adv. Nonlinear Anal.,2020

5. Global well-posedness of solutions for fourth order dispersive wave equation with nonlinear weak damping, linear strong damping and logarithmic nonlinearity;Chen;Nonlinear Anal.,2020

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. О разрешимости краевой задачи для одного класса нелинейных систем дифференциальных уравнений с частными производными высокого порядка;Математический сборник;2024

2. Well-Posedness and Dynamical Properties for Extensible Beams with Nonlocal Frictional Damping and Polynomial Nonlinearity;Applied Mathematics & Optimization;2023-10-24

3. Instability analysis and regularization approximation to the forward/backward problems for fractional damped wave equations with random noise;Applied Numerical Mathematics;2023-01

4. Continuous dependence on initial data and high energy blowup time estimate for porous elastic system;Communications in Analysis and Mechanics;2023

5. THE BOUNDARY VALUE PROBLEM FOR ONE CLASS OF HIGHER-ORDER SEMILINEAR PARTIAL DIFFERENTIAL EQUATIONS;Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan;2023