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L2-blowup estimates of the wave equation and its application to local energy decay.

Authors :
Ikehata, Ryo
Source :
Journal of Hyperbolic Differential Equations; Mar2023, Vol. 20 Issue 1, p259-275, 17p
Publication Year :
2023

Abstract

We consider the Cauchy problems in R n for the wave equation with a weighted L 1 -initial data. We derive sharp infinite time blowup estimates of the L 2 -norm of solutions in the case of n = 1 and n = 2. Then, we apply it to the local energy decay estimates for n = 2 , which is not studied so completely when the 0 th moment of the initial velocity does not vanish. The idea to derive them is strongly inspired from a technique used in [R. Ikehata, Asymptotic profiles for wave equations with strong damping, J. Differ. Equ. 257 (2014) 2159–2177; R. Ikehata and M. Onodera, Remarks on large time behavior of the L 2 -norm of solutions to strongly damped wave equations, Differ. Integral Equ. 30 (2017) 505–520]. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02198916
Volume :
20
Issue :
1
Database :
Complementary Index
Journal :
Journal of Hyperbolic Differential Equations
Publication Type :
Academic Journal
Accession number :
163820136
Full Text :
https://doi.org/10.1142/S021989162350008X