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- W3103042238 abstract "We study in this article the blow-up of the solution of the generalized Tricomi equation in the presence of two mixed nonlinearities, namely we consider $$ (Tr) hspace{1cm} u_{tt}-t^{2m}Delta u=|u_t|^p+|u|^q, quad mbox{in} mathbb{R}^Ntimes[0,infty),$$ with small initial data, where $mge0$. For the problem $(Tr)$ with $m=0$, which corresponds to the uniform wave speed of propagation, it is known that the presence of mixed nonlinearities generates a new blow-up region in comparison with the case of a one nonlinearity ($|u_t|^p$ or $|u|^q$). We show in the present work that the competition between the two nonlinearities still yields a new blow region for the Tricomi equation $(Tr)$ with $mge0$, and we derive an estimate of the lifespan in terms of the Tricomi parameter $m$. As an application of the method developed for the study of the equation $(Tr)$ we obtain with a different approach the same blow-up result as in cite{Lai2020} when we consider only one time-derivative nonlinearity, namely we keep only $|u_t|^p$ in the right-hand side of $(Tr)$." @default.
- W3103042238 created "2020-11-23" @default.
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- W3103042238 date "2020-11-06" @default.
- W3103042238 modified "2023-09-23" @default.
- W3103042238 title "Blow-up and lifespan estimate for the generalized Tricomi equation with mixed nonlinearities" @default.
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