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

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.