一类具有基尔霍夫型弱阻尼和对数非线性项的半线性波动方程  

On a Semilinear Wave Equation with Kirchhoff-type Weak Damping Terms and Logarithmic Nonlinearity

作　　者：杨怡 方钟波[1] YANG Yi;FANG Zhongbo(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：《应用数学》2022年第3期511-523,共13页Mathematica Applicata

基　　金：山东省自然科学基金面上项目(ZR2019MA072);中央高校基本科研基金(201964008)。

摘　　要：本文研究一类具有基尔霍夫型弱阻尼和对数非线性项的半线性波动方程齐次Dirichlet初边值问题解的适定性及定性性质.借助于正则解的适定性并结合稠密性理论导出局部弱解的适定性,且利用修正能量泛函技巧,建立当p <γ时整体适定性.同时,利用反证技巧,证明当p>γ时解的有限时刻爆破现象.Under homogeneous Dirichlet conditions,the well-posedness and qualitative properties for a semilinear wave equation with Kirchhoff-type weak damping terms and logarithmic nonlinearity were considered.By improving the well-posedness for regular solution and density argument,a local existence of weak solutions was proved.Meanwhile,based on modified energy technique and contradiction argument,a global existence with p <γ and the finite time blow-up with p> γ were also established.

关 键 词：半线性波动方程 基尔霍夫型弱阻尼 对数非线性 整体适定性 爆破 

分 类 号：O175.29[理学—数学]