具有非线性强阻尼和时滞项的Petrovsky方程的适定性和稳定性结果
Well-posedness and Stabiliy result of Petrovsky equation with a nonlinear strong damping and delay term
摘要：
本文考虑有界区域上具有时滞项和强耗散\begin{align*} u_{tt} + Δ^{2} u -μ_1g_1( Δ( u_t(x,t))) -μ_2g_2( Δ(u_t(x,t-τ))) =0. \end{align*}的非线性Petrovsky方程，在反馈中时滞项的权和无时滞项的权的条件下，利用能量方法和Faedo-Galarkin方法证明了在适当的索伯列夫空间中整体解的存在性.此外，我们利用凸函数的一些性质研究了一般稳定性估计。
英文摘要：
In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + Δ^{2} u -μ_1g_1( Δ( u_t(x,t))) -μ_2g_2( Δ(u_t(x,t-τ))) =0. \end{align*} We prove the existence of global solutions in suitable Sobolev spaces by using the energy method combined with Faedo-Galarkin method under condition on the weight of the delay term in the feedback and the weight of the term without delay. Furthermore, we study general stability estimates by using some properties of convex functions.
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