Behavior as t → ∞ of Solutions of a Mixed Problem for a Hyperbolic Equation with Periodic Coefficients on the Semi-Axis

被引：5

作者：

Matevossian, Hovik A. ^{[1
,2
]}

Smirnov, Vladimir Yu. ^{[2
]}

机构：

[1] Russian Acad Sci, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia

[2] Natl Res Univ MAI, Moscow Aviat Inst, Inst 3, Moscow 125993, Russia

来源：

SYMMETRY-BASEL | 2023年 / 15卷 / 03期

关键词：

asymptotic behavior; hyperbolic equation; periodic coefficients; initial boundary value problem; Schrodinger operator; ASYMPTOTIC-BEHAVIOR; CAUCHY-PROBLEM;

D O I：

10.3390/sym15030777

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we consider the asymptotic behavior (as t -> infinity) of solutions as an initial boundary value problem for a second-order hyperbolic equation with periodic coefficients on the semi-axis (x>0). The main approach to studying the problem under consideration is based on the spectral theory of differential operators, as well as on the properties of the spectrum (sigma(H-0)) of the one-dimensional Schrodinger operator H-0 with periodic coefficients p(x) and q(x).

引用

页数：22

共 32 条

[1] About a question of intrinsic value theory. [J].

Ambarzumian, V. .

ZEITSCHRIFT FUR PHYSIK, 1929, 53 (9-10) :690-695

[2] ASYMPTOTIC-BEHAVIOR AS T-]+INFINITY OF THE SOLUTIONS OF LINEAR HYPERBOLIC-EQUATIONS WITH COEFFICIENTS DISCONTINUOUS IN TIME (ON A BOUNDED DOMAIN) [J].

AROSIO, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1981, 39 (02) :291-309

[3] STURM-LIOUVILLE EIGENVALUES VIA A PHASE FUNCTION [J].

BAILEY, PB .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1966, 14 (02) :242-&

[4]

Coddington E. A., 1955, Theory of ordinary differential equations

[5]

Eastham M. S. P., 1973, The spectral theory of periodic differential equations

[6] SCHRODINGER EQUATION WITH A PERIODIC POTENTIAL [J].

EASTHAM, MSP .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURG SECTION A-MATHEMATICAL AND PHYSICAL SCIENCES, 1971, 69 :125-&

[7] FLOQUET SOLUTIONS FOR THE 1-DIMENSIONAL QUASI-PERIODIC SCHRODINGER-EQUATION [J].

ELIASSON, LH .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 146 (03) :447-482

[8]

Firsova N.E., 1986, MAT SBORN, V130, P349, DOI [10.1070/SM1987v058n02ABEH003108, DOI 10.1070/SM1987V058N02ABEH003108]

[9] DETERMINATION OF A HILLS EQUATION FROM ITS SPECTRUM [J].

GOLDBERG, W .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1975, 51 (03) :705-723

[10] Impurity bands and quasi-Bloch waves for a one-dimensional model of modulated crystal [J].

Gosse, Laurent .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2008, 9 (03) :927-948

← 1 2 3 4 →