On linear and nonlinear heat equations in degenerating domains

被引：0

作者：

Jenaliyev, M. ^{[1
]}

Ramazanov, M. ^{[2
,3
]}

Yergaliyev, M. ^{[1
]}

机构：

[1] Inst Math & Math Modeling, Pushkin Str 125, Alma Ata 050010, Kazakhstan

[2] EA Buketov Karaganda State Univ, Univ Skaya Str 28A, Karaganda 100028, Kazakhstan

[3] Inst Appl Math, Univ Skaya Str 28A, Karaganda 100028, Kazakhstan

来源：

PROCEEDINGS OF THE 43RD INTERNATIONAL CONFERENCE APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'17) | 2017年 / 1910卷

关键词：

D O I：

10.1063/1.5013968

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Earlier we studied the homogeneous boundary value problem for the heat equation in degenerating domains. For this problem in the weight class of essentially bounded functions it was established the existence of a nontrivial solution up to a constant multiplier. In this paper, on the basis of the above result, we study the issues of the existence of nontrivial solutions of homogeneous nonlinear heat equations, including the homogeneous Burgers equation in degenerating domains. The nonhomogeneous boundary value problems for the Burgers equation are studied separately.

引用

页数：10

共 50 条

[41] Linear second-order differential equations with degenerating coefficient of the second derivative [J].

V. P. Arkhipov .

Differential Equations, 2011, 47 :1397-1407

[42] On the Hölder continuity of solutions to nonlinear parabolic equations degenerating on part of the domain [J].

M. D. Surnachev .

Doklady Mathematics, 2015, 92 :412-416

[43] Asymptotics for nonlinear heat equations [J].

Hayashi, Nakao ;

Naumkin, Pavel I. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (05) :1585-1595

[44] PROBLEM E FOR A CERTAIN CLASS OF DEGENERATING NON-LINEAR ELLIPTIC EQUATIONS [J].

ALIEV, MI .

DOKLADY AKADEMII NAUK SSSR, 1967, 176 (01) :13-&

[45] NONLINEAR-WAVE EQUATIONS IN EXTERIOR DOMAINS [J].

DATTI, PS .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (04) :321-331

[46] Nonlinear diffusion equations on bounded fractal domains [J].

Hu, JX .

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2001, 20 (02) :331-345

[47] Nonlinear diffusion equations on unbounded fractal domains [J].

Falconer, KJ ;

Hu, JX .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 256 (02) :606-624

[48] Fully nonlinear elliptic equations on general domains [J].

Bao, JG .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2002, 54 (06) :1121-1141

[49] Correctors for the Nonlinear Wave Equations in Perforated Domains [J].

Zhanying Yang ;

Yunxia Yu .

Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41 :1343-1359

[50] Nonhomogeneous nonlinear integral equations on bounded domains [J].

Yi, Xing .

AIMS MATHEMATICS, 2023, 8 (09) :22207-22224

← 1 2 3 4 5 →