LOCAL EXISTENCE FOR A VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH THE DISPERSIVE TERM, INTERNAL DAMPING, AND LOGARITHMIC NONLINEARITY

被引：2

作者：

Cordeiro, Sebastiao ^{[1
]}

Raposo, Carlos ^{[2
]}

Ferreira, Jorge ^{[3
]}

Rocha, Daniel ^{[4
]}

Shahrouzi, Mohammad ^{[5
]}

机构：

[1] Fed Univ Para, Fac Exact Sci & Technol, R Manoel Abreu, BR-68440000 Abaetetuba, Para, Brazil

[2] Fed Univ Bahia Dept, Dept Math, Ave Milton Santos, BR-40170110 Salvador, BA, Brazil

[3] Fed Fluminense Univ, Dept Exact Sci, Ave Trabalhadores, BR-27255125 Rio De Janeiro, Brazil

[4] Fed Univ Para, Inst Exact & Nat Sci, R Augusto Correa, BR-66075110 Belem, Para, Brazil

[5] Jahrom Univ, Dept Math, GJPJ 8PW, Jahrom 7413766171, Fars Province, Iran

来源：

OPUSCULA MATHEMATICA | 2024年 / 44卷 / 01期

关键词：

viscoelastic equation; dispersive term; logarithmic nonlinearity; local existence; GLOBAL EXISTENCE; STABILITY;

D O I：

10.7494/OpMath.2024.44.1.19

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns a viscoelastic Kirchhoff-type equation with the dispersive term, internal damping, and logarithmic nonlinearity. We prove the local existence of a weak solution via a modified lemma of contraction of the Banach fixed-point theorem. Although the uniqueness of a weak solution is still an open problem, we proved uniqueness locally for specifically suitable exponents. Furthermore, we established a result for local existence without guaranteeing uniqueness, stating a contraction lemma.

引用

页码：19 / 47

页数：29

共 28 条

[21] Global existence and uniform stability of solutions for a quasilinear viscoelastic problem
Messaoudi, Salim A.
Tatar, Nasser-eddine
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2007, 30 (06) : 665 - 680
[22] Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms
Mezouar, Nadia
Boulaaras, Salah Mahmoud
Allahem, Ali
[J]. COMPLEXITY, 2020, 2020
[23] Nishihara K., 1984, TOKYO J MATH, V7, P437
[24] Degenerate Kirchhoff-type wave problems involving the fractional Laplacian with nonlinear damping and source terms
Pan, Ning
Pucci, Patrizia
Xu, Runzhang
Zhang, Binlin
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2019, 19 (03) : 615 - 643
[25] Pohozaev S. I., 1975, MATH USSR SB, V25, P145, DOI DOI 10.1070/SM1975V025N01ABEH002203
[26] Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation
Wang, Xingchang
Xu, Runzhang
[J]. ADVANCES IN NONLINEAR ANALYSIS, 2021, 10 (01) : 261 - 288
[27] Kirchhoff-type system with linear weak damping and logarithmic nonlinearities
Wang, Xingchang
Chen, Yuxuan
Yang, Yanbing
Li, Jiaheng
Xu, Runzhang
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 188 : 475 - 499
[28] Weir A.J, 1973, Lebesque Integration and Measure, Reader in Mathematics and Education

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