Microlocal partition of energy for linear wave or Schrodinger equations

被引：2

作者：

Delort, Jean -Marc ^{[1
]}

机构：

[1] Univ Paris XIII Sorbonne Paris Nord, Dept Math, Villetaneuse, France

来源：

TUNISIAN JOURNAL OF MATHEMATICS | 2022年 / 4卷 / 02期

基金：

美国国家科学基金会;

关键词：

wave equation; Schr?dinger equation; channels of energy; microlocal analysis;

D O I：

10.2140/tunis.2022.4.329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a microlocal partition of energy for solutions to linear half-wave or Schrodinger equations in any space dimension. This extends well-known (local) results valid for the wave equation outside the wave cone, and allows us in particular, in the case of even dimension, to generalize the radial estimates due to Cote, Kenig and Schlag to nonradial initial data.

引用

页码：329 / 385

页数：58

共 50 条

[41] Energy decay estimate for the boundary stabilization of the coupled wave equations
Najafi, M.
MATHEMATICAL AND COMPUTER MODELLING, 2008, 48 (11-12) : 1796 - 1805
[42] A note on local energy decay results for wave equations with a potential
Ikehata, Ryo
ASYMPTOTIC ANALYSIS, 2023, 134 (1-2) : 281 - 295
[43] Some examples causing energy growth for solutions to wave equations
Wakasugi, Yuta
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2011, 87 (08) : 136 - 141
[44] Attractors for a class of wave equations with nonlocal structural energy damping
Bezerra, Flank D. M.
Liu, Linfang
Narciso, Vando
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2024, 31 (06):
[45] Observability and stabilization of magnetic Schrodinger equations
Ammari, Kais
Choulli, Mourad
Robbiano, Luc
JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 267 (05) : 3289 - 3327
[46] Kinetic energy based relativistic first order wave equations
Umul, Yusuf Ziya
OPTIK, 2019, 181 : 320 - 325
[47] $L^p$ estimates for the linear wave equation and global existence for semilinear wave equations in exterior domains
Mitsuhiro Nakao
Mathematische Annalen, 2001, 320 : 11 - 31
[48] Energy dissipation for hereditary and energy conservation for non-local fractional wave equations
Zorica, Dusan
Oparnica, Ljubica
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2020, 378 (2172):
[49] Time-dependent attractor of wave equations with nonlinear damping and linear memory
Ma, Qiaozhen
Wang, Jing
Liu, Tingting
OPEN MATHEMATICS, 2019, 17 : 89 - 103
[50] Critical counterexamples for linear wave equations with time-dependent propagation speed
Ghisi, Marina
Gobbino, Massimo
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (12) : 11435 - 11460

← 1 2 3 4 5 →