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

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