Some results on the global solvability for structurally damped models with a special nonlinearity

• Date: 2018
• Main Authors: Duong, P. T., Дуонг, П. Т.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2018
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1629
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The main purpose of this paper is to prove the global (in time) existence of solution for the semilinear Cauchy problem $$u_{tt} + (-\Delta )^{\sigma} u + (-\Delta )^{\delta} u_t = |u_t|^p,\; u(0, x) = u_0(x),\; u_t(0, x) = u_1(x)$$. The parameter $\delta \in (0, \sigma]$ describes the structural...