GLOBAL ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO QUASILINEAR SCHRODINGER EQUATIONS

被引：0

作者：

Zhang, Lin ^{[1
]}

Song, Xianfa ^{[2
]}

机构：

[1] Tianjin Univ, Ctr Appl Math, Sch Math, Tianjin 300072, Peoples R China

[2] Tianjin Univ, Sch Math, Dept Math, Tianjin 300072, Peoples R China

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年

基金：

中国国家自然科学基金;

关键词：

Qusilinear Schrodinger equation; global solution; blow up; asymptotic behavior; LOCAL WELL-POSEDNESS; STANDING WAVES; CAUCHY-PROBLEM; STABILITY; SOLITONS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the existence and blowup of solutions for a class of quasilinear Schrodinger equations. In particular, we examine the combined effect of local type nonlinearity and Hartree type ones, and depending upon different parameter regimes, we find the dominant roles exhibited by these nonlinear effects. We also consider the asymptotic behavior for the global solution and lower bound for the blowup rate of the blowup solution by using pseudo-conformal conservation laws.

引用

页数：14

共 21 条

[1] NONLINEAR ELECTROMAGNETIC-SPIN WAVES [J].

BASS, FG ;

NASONOV, NN .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1990, 189 (04) :165-223

[2]

Borovskii A. V., 1993, Journal of Experimental and Theoretical Physics, V77, P562

[3]

Cazenave T., 2003, SEMILINEAR SCHRODING

[4] Stability of standing waves for a class of quasilinear Schrodinger equations [J].

Chen, Jianqing ;

Li, Yongqing ;

Wang, Zhi-Qiang .

EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2012, 23 :611-633

[5] NECESSARY AND SUFFICIENT CONDITIONS FOR SELF-FOCUSING OF SHORT ULTRAINTENSE LASER-PULSE IN UNDERDENSE PLASMA [J].

CHEN, XL ;

SUDAN, RN .

PHYSICAL REVIEW LETTERS, 1993, 70 (14) :2082-2085

[6] On the local well-posedness of quasilinear Schrodinger equations in arbitrary space dimension [J].

Colin, M .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (1-2) :325-354

[7] Stability and instability results for standing waves of quasi-linear Schrodinger equations [J].

Colin, Mathieu ;

Jeanjean, Louis ;

Squassina, Marco .

NONLINEARITY, 2010, 23 (06) :1353-1385

[8] Global existence of small solutions to a relativistic nonlinear Schrodinger equation [J].

deBouard, A ;

Hayashi, N ;

Saut, JC .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 189 (01) :73-105

[9] BLOWING UP OF SOLUTIONS TO CAUCHY-PROBLEM FOR NONLINEAR SCHRODINGER EQUATIONS [J].

GLASSEY, RT .

JOURNAL OF MATHEMATICAL PHYSICS, 1977, 18 (09) :1794-1797

[10] The "Blow up" problem for a quasilinear Schrodinger equation [J].

Guo, BL ;

Chen, JQ ;

Su, FQ .

JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (07)

← 1 2 3 →