Classical solutions for 1-dimensional and 2-dimensional Boussinesq equations

被引：0

作者：

Georgiev, Svetlin ^{[1
]}

Boukarou, Aissa ^{[2
]}

Zennir, Khaled ^{[3
]}

机构：

[1] Univ Sofia, Dept Math, Fac Math & Informat, Sofia, Bulgaria

[2] Univ Ghardaia, Fac Math & Informat, Dept Math, Ghardaia, Algeria

[3] Qassim Univ, Coll Sci & Arts, Dept Math, Ar Rass, Saudi Arabia

来源：

TURKISH JOURNAL OF MATHEMATICS | 2022年 / 46卷 / 07期

关键词：

Boussinesq equation; existence; classical solution; WELL-POSEDNESS;

D O I：

10.55730/1300-0098.3313

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we investigate the IVPs for 1-dimensional and 2-dimensional Boussinesq equations. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions for the considered IVPs. The arguments are based upon recent theoretical results.

引用

页码：2977 / 2997

页数：21

共 13 条

[1]

[Anonymous], 1993, Geom. Funct. Anal.

[2]

[Anonymous], 2007, Methods of nonlinear analysis: Applications to differential equations

[3]

[Anonymous], 1980, Measure of Noncompactness in Banach Spaces

[4] FIXED POINT INDEX THEORY FOR PERTURBATION OF EXPANSIVE MAPPINGS BY k-SET CONTRACTIONS [J].

Djebali, Smail ;

Mebarki, Karima .

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2019, 54 (02) :613-640

[5] Local well-posedness for the sixth-order Boussinesq equation [J].

Esfahani, Amin ;

Farah, Luiz Gustavo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 385 (01) :230-242

[6] Local Solutions in Sobolev Spaces with Negative Indices for the Good Boussinesq Equation [J].

Farah, Luiz Gustavo .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2009, 34 (01) :52-73

[7] Existence of solutions for a class of nonlinear impulsive wave equations [J].

Georgiev, Svetlin G. ;

Zennir, Khaled .

RICERCHE DI MATEMATICA, 2022, 71 (01) :211-225

[8]

Kadomtsev B. B., 1970, Soviet Physics - Doklady, V15, P539

[9] On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking [J].

Manakov, S. V. ;

Santini, P. M. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (05)

[10] 2-DIMENSIONAL SOLITONS OF KADOMTSEV-PETVIASHVILI EQUATION AND THEIR INTERACTION [J].

MANAKOV, SV ;

ZAKHAROV, VE ;

BORDAG, LA ;

ITS, AR ;

MATVEEV, VB .

PHYSICS LETTERS A, 1977, 63 (03) :205-206

← 1 2 →