Local existence for a viscoelastic kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity
OPUSCULA MATHEMATICA(2024)
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.
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Key words
viscoelastic equation,dispersive term,logarithmic nonlinearity,local existence
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