TY  - JOUR
ID  - Cordeiro2024
LB  - Cordeiro2024
AU  - Cordeiro, Sebastião
AU  - Raposo, Carlos
AU  - Ferreira, Jorge
AU  - Rocha, Daniel
AU  - Shahrouzi, Mohammad
TI  - Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity
ST  - Local existence for a viscoelastic Kirchhoff type equation with the dispersive term, internal damping, and logarithmic nonlinearity
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 1
SP  - 19
EP  - 47
DO  - https://doi.org/10.7494/OpMath.2024.44.1.19
UR  - https://doi.org/10.7494/OpMath.2024.44.1.19
AB  - 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.
KW  - viscoelastic equation
KW  - dispersive term
KW  - logarithmic nonlinearity
KW  - local existence
SN  - 1232-9274
ER  -