Open AccessExistence and Continuous Dependence of the Local Solution of Non-Homogeneous KdV-K-S Equation in Periodic Sobolev Spaces
Author(s) -
Yolanda Silvia Santiago Ayala,
AUTHOR_ID,
Santiago César Rojas Romero
Publication year - 2021
Publication title -
journal of mathematical sciences : advances and applications
Language(s) - English
Resource type - Journals
ISSN - 0974-5750
DOI - 10.18642/jmsaa_7100122161
Subject(s) - korteweg–de vries equation , sobolev space , mathematics , homogeneous , uniqueness , dissipative system , mathematical analysis , initial value problem , type (biology) , work (physics) , pure mathematics , physics , combinatorics , thermodynamics , ecology , quantum mechanics , nonlinear system , biology
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].