Nonexistence of Global Solutions to A Semilinear Wave Equation with Scale Invariant Damping
Changwang Xiao *
School of Mathematical Sciences, Nanjing Normal University Nanjing 210023, China.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Semilinear wave equations, tricomi equation, structural damping, nite time blow up, critical power