Existence and Continuous Dependence of the Local Solution of Non-Homogeneous KdV-K-S Equation in Periodic Sobolev Spaces
Universidad Nacional Mayor de San Marcos, Yolanda Silvia Santiago Ayala, Santiago César Rojas Romero
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].
Topics & Concepts
Korteweg–de Vries equationSobolev spaceMathematicsHomogeneousUniquenessDissipative systemMathematical analysisInitial value problemType (biology)Work (physics)Pure mathematicsPhysicsCombinatoricsThermodynamicsQuantum mechanicsEcologyBiologyNonlinear systemAdvanced Mathematical Physics ProblemsNonlinear Waves and Solitons