Open AccessNonexistence of Global Solutions to A Semilinear Wave Equation with Scale Invariant Damping
Author(s) -
Changwang Xiao
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i830387
Subject(s) - lemma (botany) , wave equation , mathematics , invariant (physics) , dissipation , scale invariance , mathematical analysis , scale (ratio) , mathematical physics , physics , statistics , ecology , poaceae , quantum mechanics , biology , thermodynamics
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.