论文标题
与对数非线性阻尼四阶波方程的解决方案的寿命
Lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity
论文作者
论文摘要
本文将解决方案的寿命致力于具有对数非线性$$ U_ u_ u_ {tt}+Δ^2U-δ^2U-δU-δU-δU_T+α（T）U_T+α（t）u_t = | U | U | U | U | U | U | U |每种情况都给出了爆炸时间的绑定。此外，通过构建新的辅助功能并充分利用强阻尼术语，也得出了爆破时间的下限。
This paper is devoted to the lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity $$u_{tt}+Δ^2u-Δu-ωΔu_t+α(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up criteria for solutions at both lower and high initial energy levels are established, and an upper bound for the blow-up time is given for each case. Moreover, by constructing a new auxiliary functional and making full use of the strong damping term, a lower bound for the blow-up time is also derived.
