Blow-Up of Solutions to Von Karman Equations with Arbitrary Initial Energy

被引：1

作者：

Li, Lijuan ^{[1
]}

Zhou, Jun ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 02期

关键词：

Von Karman equations; variable exponents; blow-up; THIN ELASTIC PLATE; SPACES;

D O I：

10.1007/s00009-023-02329-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The blow-up of solutions to Von Karman equations with arbitrary initial energy is proved. The proof is based on energy estimates, Lebesgue and Sobolev spaces with variable exponents, and ordinary differential inequalities. The results of this paper generalize the previous blow-up results of this model. More precisely, we show the existence of finite time blow-up solutions with arbitrary initial energy whereas the previous results were given when the initial energy was less than a positive constant.

引用

页数：13

共 24 条

[1]

Alshin A. B., 2011, De Gruyter Series in Nonlinear Analysis and Applications, V15, DOI [10.1515/9783110255294, DOI 10.1515/9783110255294]

[2]

Antontsev SN., 2015, Evolution PDEs with nonstandard growth conditions, DOI [10.2991/978-94-6239-112-3, DOI 10.2991/978-94-6239-112-3]

[3] VON KARMANS EQUATIONS AND BUCKLING OF A THIN ELASTIC PLATE 2 PLATE WITH GENERAL EDGE CONDITIONS [J].

BERGER, MS ;

FIFE, PC .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1968, 21 (03) :227-&

[4] ON VON KARMANS EQUATIONS AND BUCKLING OF A THIN ELASTIC PLATE .I. CLAMPED PLATE [J].

BERGER, MS .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1967, 20 (04) :687-&

[5] EXISTENCE OF EQUILIBRIUM STATES OF THIN ELASTIC SHELLS .1. [J].

BERGER, MS .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1971, 20 (07) :591-&

[6]

Cherrier P., 2015, EVOLUTION EQUATIONS, DOI [10.1007/978-3-319-20997-5, DOI 10.1007/978-3-319-20997-5]

[7]

Chueshov I, 2010, SPRINGER MONOGR MATH, P1, DOI 10.1007/978-0-387-87712-9

[8]

Ciarlet PG., 1980, QUATIONS K RM N, DOI [10.1007/BFb0091528, DOI 10.1007/BFB0091528]

[9] Lebesgue and Sobolev Spaces with Variable Exponents [J].

Diening, Lars ;

Harjulehto, Petteri ;

Hasto, Peter ;

Ruzicka, Michael .

LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+

[10] On the spaces Lp(x)(Ω) and Wm, p(x)(Ω) [J].

Fan, XL ;

Zhao, D .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 263 (02) :424-446

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