Remark on One Dimensional Semilinear Damped Wave Equation in a Critical Weighted L 2-space

Motohiro Sobajima,Yuta Wakasugi

doi:10.1007/978-3-030-73363-6_14

Remark on One Dimensional Semilinear Damped Wave Equation in a Critical Weighted L 2-space

Motohiro Sobajima, Yuta Wakasugi

https://doi.org/10.1007/978-3-030-73363-6_14

Copy DOI

Publication Date: Feb 24, 2012

Citations: 2

Affiliation: Tokyo University of Science, Hiroshima University

#Semilinear Damped Wave Equation #Weighted Hardy Inequality + Show 8 more

Abstract
Full-Text PDF
Similar Papers

Abstract

We study the Cauchy problem of the semilinear damped wave equation in one space dimension. We show the existence of global solutions in the critical case with small initial data in weighted L2-spaces. This problem in multidimensional cases was dealt with in Sobajima (Differ Integr Equ 32:615–638, 2019) via the weighted Hardy inequality which is false in one-dimension. The crucial idea of the proof is the use of an incomplete version of Hardy inequality.

Full Text