In this paper, we consider a one-dimension semilinear wave equation with a time-dependent damping and power type nonlinearity, which only depends on the derivatives of the unknown function. Employing the global iteration method, we give a simple proof of the global existence of the small data classical solution to the equation for any given nonlinear power exponent which is bigger than 1.
We obtain a blowup result for solutions to a semilinear wave equation with scale-invariant dissipation. We perform a change of variables that transforms our starting equation into a Generalized Tricomi equation, then apply Kato’s lemma, we can prove a blowup result for solutions to the transformed equation under some assumptions on the initial data. In the critical case, we use the fundamental solutions of the Generalized Tricomi equation to modify Kato’s lemma to deal with it.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.