Addoun, Rayan IkramLaoubi, Karima2024-07-232024-07-2320240020-7179https://www.tandfonline.com/doi/full/10.1080/00207179.2024.2368052https://doi.org/10.1080/00207179.2024.2368052https://dspace.univ-boumerdes.dz/handle/123456789/14222This paper primarily focuses on analysing the exponential decay stability and regularity of the solution to a nonlinear wave equation with localised internal damping, characterised by a Carathéodory function and Ventcel-Dirichlet boundary conditions. Additionally, the regularity of the solution within this framework is investigated. Stability through exponential decay is established by formulating fresh Lyapunov functions and employing multiplier techniques. It's essential to underline the recognition of the memory term's influence at the boundary on the solution, thereby introducing a degree of uncertainty into the analysis.en35B3535B4035L05Exponential decay stabilitylocalised internal dampingNonlinear wave equationRegularity; Ventcel boundary conditionsArticle