Regularity and decay of solutions to the stark evolution equation

被引：9

作者：

Ben-Artzi, M ^{[1
]}

Devinatz, A

机构：

[1] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

[2] Northwestern Univ, Dept Math, Evanston, IL 60208 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1998年 / 154卷 / 02期

关键词：

Stark Hamiltonian; global regularity; long-time decay;

D O I：

10.1006/jfan.1997.3211

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Long-time behavior and regularity are studied for solutions of the Stark equation u(1) = i(- Delta - x(1) + V(x)) u, u(O, x) is an element of L-2(R-n). It is shown that for a class of short-range potentials V(x) the gain of local smoothness and the decay as \t\ --> infinity are close to those of the corresponding Schrodinger equation u(1) = i(- Delta + V(x))u. (C) 1998 Academic Press.

引用

页码：501 / 512

页数：12

共 19 条

[1] SPECTRAL AND SCATTERING THEORY OF SCHRODINGER OPERATORS RELATED TO STARK EFFECT [J].

AVRON, JE ;

HERBST, IW .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 52 (03) :239-254

[2] UNITARY EQUIVALENCE AND SCATTERING-THEORY FOR STARK-LIKE HAMILTONIANS [J].

BENARTZI, M .

JOURNAL OF MATHEMATICAL PHYSICS, 1984, 25 (04) :951-964

[3] GLOBAL ESTIMATES FOR THE SCHRODINGER-EQUATION [J].

BENARTZI, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 1992, 107 (02) :362-368

[4] DECAY AND REGULARITY FOR THE SCHRODINGER-EQUATION [J].

BENARTZI, M ;

KLAINERMAN, S .

JOURNAL D ANALYSE MATHEMATIQUE, 1992, 58 :25-37

[5]

BenArtzi M, 1997, ANN I H POINCARE-PHY, V67, P29

[6] LOCAL SMOOTHING AND CONVERGENCE PROPERTIES OF SCHRODINGER TYPE EQUATIONS [J].

BENARTZI, M ;

DEVINATZ, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 101 (02) :231-254

[7]

BENARTZI M, 1984, J ANAL MATH, V43, P215

[8]

BENARTZI M, 1987, MEMOIRS AM MATH SOC, V364

[9] LOCAL SMOOTHING PROPERTIES OF SCHRODINGER-EQUATIONS [J].

CONSTANTIN, P ;

SAUT, JC .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1989, 38 (03) :791-810

[10]

Constantin P., 1988, J AM MATH SOC, V1, P413

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