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Browsing by Author "Raposo, Carlos"

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    Item type:Article, Access status: Open Access ,
    Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity
    (Wydawnictwa AGH, 2024) Cordeiro, Sebastião; Raposo, Carlos; Ferreira, Jorge; Rocha, Daniel; Shahrouzi, Mohammad
    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.