The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case

In this paper, we study the Cauchy problem for linear and semilinear Moore-Gibson-Thompson (MGT) equation in dissipative case. Concerning MGT model, by utilizing WKB analysis associated with Fourier analysis, derive some $L^2$ estimates of solutions, which improve those previous research [46]. Furthermore, asymptotic profiles solution an approximate relation a framework weighted $L^1$ space are derived. Next, aid classical energy method Hardy's inequality, get singular limit results itself. basing on these sharp constructing time-weighted Sobolev spaces, investigate global (in time) existence solutions different regularities. Finally, under sign assumption initial data, nonexistence weak is proved applying test function method.