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

被引：9

作者：

Ikehata, Ryo ^{[1
]}

机构：

[1] Hiroshima Univ, Grad Sch Humanities & Social Sci, Dept Math, Div Educ Sci, Higashihiroshima 7398524, Japan

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2023年 / 20卷 / 01期

关键词：

Wave equation; weighted L-1 ??????? data; local energy; low dimension; blowup in infinite time; sharp estimates; BOUNDARY VALUE-PROBLEM; HYPERBOLIC-EQUATIONS; EXTERIOR PROBLEM; 2ND-ORDER; SYSTEMS;

D O I：

10.1142/S021989162350008X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problems in R-n for the wave equation with a weighted L1-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 0th 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].

引用

页码：259 / 275

页数：17

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