LOCAL ENERGY DECAY AND SMOOTHING EFFECT FOR THE DAMPED SCHRODINGER EQUATION

被引：3

作者：

Khenissi, Moez ^{[1
]}

Royer, Julien ^{[2
]}

机构：

[1] Univ Sousse, LAMMDA, Ecole Super Sci & Technol Hammam Sousse, Rue Lamine El Abbessi, Hammam Sousse 4011, Tunisia

[2] Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse 9, France

来源：

ANALYSIS & PDE | 2017年 / 10卷 / 06期

关键词：

local energy decay; smoothing effect; damped Schrodinger equation; resolvent estimates; WAVE-EQUATION; EXPONENTIAL DECAY; EXTERIOR; STABILIZATION; ABSENCE; REGULARITY; RESOLVENT;

D O I：

10.2140/apde.2017.10.1285

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the local energy decay and the global smoothing effect for the damped Schrodinger equation on R-d. The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation that we consider.

引用

页码：1285 / 1315

页数：31

共 50 条

[1] Local energy decay for the damped wave equation
Bouclet, Jean-Marc
Royer, Julien
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (07) : 4538 - 4615
[2] On the local smoothing for the Schrodinger equation
Vega, Luis
Visciglia, Nicola
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (01) : 119 - 128
[3] LOCAL DECAY FOR THE DAMPED WAVE EQUATION IN THE ENERGY SPACE
Royer, Julien
[J]. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2018, 17 (03) : 509 - 540
[4] Local smoothing effect on the Schrodinger equation with harmonic potential
Fang, Daoyuan
Han, Zheng
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (01) : 28 - 40
[5] LOCAL ENERGY DECAY FOR THE DAMPED PLATE EQUATION IN EXTERIOR DOMAINS
SONG, J
[J]. QUARTERLY OF APPLIED MATHEMATICS, 1992, 50 (02) : 257 - 272
[6] A local smoothing estimate for the Schrodinger equation
Rogers, Keith M.
[J]. ADVANCES IN MATHEMATICS, 2008, 219 (06) : 2105 - 2122
[7] Asymptotic smoothing effect for a weakly damped nonlinear Schrodinger equation in T2
Goubet, O
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 165 (01) : 96 - 122
[8] Energy decay estimates for the damped plate equation with a local degenerated dissipation
Guzmán, RB
Tuesnak, M
[J]. SYSTEMS & CONTROL LETTERS, 2003, 48 (3-4) : 191 - 197
[9] LOCAL SMOOTHING FOR THE SCHRODINGER EQUATION WITH A PRESCRIBED LOSS
Christianson, Hans
Wunsch, Jared
[J]. AMERICAN JOURNAL OF MATHEMATICS, 2013, 135 (06) : 1601 - 1632
[10] Decay of local energy for solutions of the free Schrodinger equation in exterior domains
Burq, N.
Ducomet, B.
[J]. KYOTO JOURNAL OF MATHEMATICS, 2020, 60 (03) : 911 - 939

← 1 2 3 4 5 →