@Article{Cordeiro2024,
author = "Cordeiro, Sebastião and Raposo, Carlos and Ferreira, Jorge and Rocha, Daniel and Shahrouzi, Mohammad",
title = "Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "1",
pages = "19--47",
doi = "https://doi.org/10.7494/OpMath.2024.44.1.19",
url = "https://doi.org/10.7494/OpMath.2024.44.1.19",
abstract = "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",
issn = "1232-9274"
}