Local well-posedness of a nonlinear KdV-type equation |
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| Authors: | Samer Israwi Raafat Talhouk |
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| Institution: | 1. Center for Research in Applied Mathematics and Statistics, Arts Sciences and Technology University in Lebanon (AUL), 113-7504 Beirut, Lebanon;2. Department and Laboratory of Mathematics, Faculty of Sciences 1, Doctoral School of Sciences and Technology, Lebanese University, Hadath, Lebanon |
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| Abstract: | In this paper, a generalized nonlinear KdV equation with time- and space-dependent coefficients is considered. We show that the control of the dispersive and “diffusion” terms is possible if we use an adequate weight function determined with respect to the dispersive and “diffusion” coefficients to define the energy. We use the dispersive properties of the equation to prove the existence and uniqueness of solutions. |
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