Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems

被引：0

作者：

Márcio Cavalcante

机构：

[1] Universidade Federal de Alagoas,Instituto de Matemática

来源：

São Paulo Journal of Mathematical Sciences | 2019年 / 13卷

关键词：

Initial boundary value problems; Nonlinear dispersive equations; Open problems; 35Q53; 35Q55; 35G31;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In the last years the study of initial boundary value problems for nonlinear dispersive equations on the half-lines has given attention of many researchers. This turns out to be a rather challenging problem, mainly when studied in low Sobolev regularity. In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view.

引用

页码：418 / 434

页数：16

共 50 条

[1] Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems
Cavalcante, Marcio
[J]. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, 2019, 13 (02): : 418 - 434
[2] Initial-boundary value problems for linear dispersive evolution equations on the half-line
Sung, LY
[J]. FIFTH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION, 2000, : 374 - 378
[3] Initial-Boundary Value Problems for the Coupled Nonlinear Schrodinger Equation on the Half-Line
Geng, Xianguo
Liu, Huan
Zhu, Junyi
[J]. STUDIES IN APPLIED MATHEMATICS, 2015, 135 (03) : 310 - 346
[4] A variational approach to some boundary value problems in the half-line
Gomes, JM
Sanchez, L
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2005, 56 (02): : 192 - 209
[5] A variational approach to some boundary value problems in the half-line
J. M. Gomes
L. Sanchez
[J]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 2005, 56 : 192 - 209
[6] The existence of three positive solutions for some nonlinear boundary value problems on the half-line
Liang, Sihua
Zhang, Jihui
[J]. POSITIVITY, 2009, 13 (02) : 443 - 457
[7] The existence of three positive solutions for some nonlinear boundary value problems on the half-line
Sihua Liang
Jihui Zhang
[J]. Positivity, 2009, 13 : 443 - 457
[8] The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line
Lin HUANG
[J]. Chinese Annals of Mathematics,Series B, 2020, (01) : 117 - 132
[9] The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line
Huang, Lin
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2020, 41 (01) : 117 - 132
[10] The Initial-Boundary-Value Problems for the Hirota Equation on the Half-Line
Lin Huang
[J]. Chinese Annals of Mathematics, Series B, 2020, 41 : 117 - 132

← 1 2 3 4 5 →