A semilinear non-homogeneous problem related to Korteweg-de Vries Equation





semilinear problem, KdV equation, existence, uniqueness, regularity, anisotropic Sobolev space


In this paper, we consider a non-homogeneous generalized Korteweg-de Vries problem with some hypotheses on the right-hand side, and we give a new regularity result of the solution in an anisotropic Sobolev space. Then we apply the obtained result to a non-homogeneous KdV problem. This work is an extension of solvability results for a right-hand side f in Lebesgue space.

Author Biography

Boubaker-Khaled Sadallah, Ecole Normale Supérieure - Kouba.

Department of Mathematics, Lab. E.D.P.N.L.


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How to Cite

Y. Benia and B.-K. Sadallah, “A semilinear non-homogeneous problem related to Korteweg-de Vries Equation”, Proyecciones (Antofagasta, On line), vol. 43, no. 2, pp. 401-423, Apr. 2024.