一类具有对数源项和应变项的半线性四阶波动方程解的高能爆破现象  

Blow-Up Phenomena for a Semilinear Fourth-Order Wave Equation with Strain Terms and Logarithmic Nonlinearity at High Energy Level

作　　者：徐文静 赵元章[1] Xu Wenjing;Zhao Yuanzhang(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2024年第11期151-156,共6页Periodical of Ocean University of China

基　　金：山东省自然科学基金项目(ZR2019MA072)资助。

摘　　要：本文侧重研究一类具有对数源项和非线性应变项的半线性四阶波动方程Dirichlet和Navier初边值问题。利用非稳定集的不变性、反证法技巧及凹性引理,给出了任意正初始能量级E(0)>0下解的高能爆破结果。This paper is concerned with the initial boundary value problem for a class of semilinear fourth-order wave equation with logarithmic nonlinearity and nonlinear strain terms under Dirichlet or Navier boundary condition.By utilizing the invariance of unstable set,contradiction argument and concavity method,we prove thatthe solution is blows up in finite time at any positive high energy levelin finite time at high energy level.

关 键 词：四阶波动方程 对数源项 应变项 高能爆破 

分 类 号：O175[理学—数学]