In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-...In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.展开更多
Let Ω R^n be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term Based on a time-uniform priori estimate method, the existence ...Let Ω R^n be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term Based on a time-uniform priori estimate method, the existence of the compact global attractor is proved for this model in the phase space H^（^） x L2（~）.展开更多
基金Supported by the Natural Science Foundation of China(Grant No.11371175)Innovation Team Project in Colleges and Universities of Guangdong Province(Grant No.2020WCXTD008)+1 种基金Science Foundation of Huashang College Guangdong University of Finance&Economics(Grant No.2020HSDS01)Science Research Team Project in Guangzhou Huashang College(Grant No.2021HSKT01).
文摘In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.
基金Supported by the National Natural Science Foundation of China (Grant No. 10471018)
文摘Let Ω R^n be a bounded domain with a smooth boundary. We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term Based on a time-uniform priori estimate method, the existence of the compact global attractor is proved for this model in the phase space H^（^） x L2（~）.
