Formation of singularities of solutions to the Cauchy problem for semilinear Moore-Gibson-Thompson equations

Abstract

This paper is devoted to investigating formation of singularities for solutions to semilinear Moore-Gibson-Thompson equations with power type nonlinearity \begin{document}$ |u|^{p} $\end{document}, derivative type nonlinearity \begin{document}$ |u_{t}|^{p} $\end{document} and combined type nonlinearities \begin{document}$ |u_{t}|^{p}+|u|^{q} $\end{document} in the case of single equation, combined type nonlinearities \begin{document}$ |v_{t}|^{p_{1}}+|v|^{q_{1}} $\end{document}, \begin{document}$ |u_{t}|^{p_{2}}+|u|^{q_{2}} $\end{document}, combined and power type nonlinearities \begin{document}$ |v_{t}|^{p_{1}}+|v|^{q_{1}} $\end{document}, \begin{document}$ |u|^{q_{2}} $\end{document}, combined and derivative type nonlinearities \begin{document}$ |v_{t}|^{p_{1}}+|v|^{q_{1}} $\end{document}, \begin{document}$ |u_{t}|^{p_{2}} $\end{document} in the case of coupled system, respectively. More precisely, blow-up results of solutions to problems in the sub-critical and critical cases are derived by applying test function technique. Moreover, upper bound lifespan estimates of solutions to the coupled systems are investigated. The main new contribution is that lifespan estimates of solutions are associated with the well-known Strauss exponent and Glassey exponent.