Existence and Continuous Dependence of the Local Solution of Non-Homogeneous KdV-K-S Equation in Periodic Sobolev Spaces

Abstract

In this article, we prove that initial value problem associated to the non-homogeneous KdV-Kuramoto-Sivashinsky (KdV-K-S) equation in periodic Sobolev spaces has a local solution in with and the solution has continuous dependence with respect to the initial data and the non-homogeneous part of the problem. We do this in an intuitive way using Fourier theory and introducing a inspired by the work of Iorio [2] and Ayala and Romero [8]. Also, we prove the uniqueness solution of the homogeneous and non-homogeneous KdV-K-S equation, using its dissipative property, inspired by the work of Iorio [2] and Ayala and Romero [9].

Trajetórias e perspectivas para a pesquisa em matemática

“…In this work we will make a complete study of the existence, uniqueness and continuous dependence of the solution of the KdV-K-S equation and its corresponding non-homogeneous problem, giving more properties, improvement of results and additional proofs. Thus, this is a unified study with improvements of [10] and [13].…”

“…) is locally well posed in compacts, obtaining continuous dependence with respect to the initial data and the non homogeneity. ,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,31,32,33,36,38,39,40,85 Educação estatística 24,25,31,33,38 Educação matemática 10,11,12,13,14,15,16,17,18,22,23,26,85 Existence of solution 54 F Fourier theory 54, 55, 83 G Gref 24,25,26,31,33,…”