Title : ( Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity )
Authors: Sebastiao Cordeiro , Carlos Raposo , Jorge Ferreira , Daniel Rocha , Mohammad Shahrouzi ,
Full TextAbstract
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.
Keywords
, viscoelastic equation, dispersive term, logarithmic nonlinearity, local existence.
@article{paperid:1098944,
author = {سباستیائو کوردیرو and کارلوس رپوسو and جرج فریرا and دنیل روشا and Shahrouzi, Mohammad},
title = {Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity},
journal = {Opuscula Mathematica},
year = {2024},
volume = {44},
number = {1},
month = {January},
issn = {1232-9274},
pages = {19--47},
numpages = {28},
keywords = {viscoelastic equation; dispersive term; logarithmic nonlinearity; local existence.},
}
%0 Journal Article
%T Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity
%A سباستیائو کوردیرو
%A کارلوس رپوسو
%A جرج فریرا
%A دنیل روشا
%A Shahrouzi, Mohammad
%J Opuscula Mathematica
%@ 1232-9274
%D 2024
