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Abstract
This paper deals with a hyperbolic-type equation with a logarithmic source term and dynamic boundary condition. Given convenient initial data, we obtained the local existence of a weak solution. Local existence results of solutions are obtained using the Faedo-Galerkin method and the Schauder fixed-point theorem. Additionally, under suitable assumptions on initial data, the lower bound time of the blow-up result is investigated.
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Details
1 Mardin Said Nursi Anatolian High School, Mardin, Turkey
2 M’Sila University, Department of Physics, Faculty of Sciences, M’Sila, Algeria (GRID:grid.442480.e) (ISNI:0000 0004 0489 9914)
3 Dicle University, Department of Mathematics, Diyarbakir, Turkey (GRID:grid.411690.b) (ISNI:0000 0001 1456 5625)
4 Qassim University, Department of Mathematics, College of Sciences and Arts in ArRass, Buraydah, Saudi Arabia (GRID:grid.412602.3) (ISNI:0000 0000 9421 8094)