Initial-Boundary Value Problems for Nonlinear Dispersive Equations of Higher Orders Posed on Bounded Intervals with General Boundary Conditions

Nikolai A Larkin,Jackson Luchesi

doi:10.3390/math9020165

Abstract

The present article concerns general mixed problems for nonlinear dispersive equations of any odd-orders posed on bounded intervals. The results on existence, uniqueness and exponential decay of solutions are presented.

Highlights

IntroductionWe formulate mixed problems with general boundary conditions for the following dispersive equation: Citation: Larkin, N.A.; Luchesi, J
In this work, we formulate mixed problems with general boundary conditions for the following dispersive equation: Citation: Larkin, N.A.; Luchesi, J.Initial-Boundary Value Problems for l ut +Intervals with General BoundaryConditions
It is known that the Korteweg-de Vries (KdV) and Kawahara equations were deduced on the whole real line, approximating the line either by bounded or unbounded intervals, one needs to consider initial-boundary value problems posed either on finite or semi-finite intervals [2,4,9,10,11,13,14,15,17,18,19,20,21,22]

Summary

Introduction

We formulate mixed problems with general boundary conditions for the following dispersive equation: Citation: Larkin, N.A.; Luchesi, J. It is known that the KdV and Kawahara equations were deduced on the whole real line, approximating the line either by bounded or unbounded intervals, one needs to consider initial-boundary value problems posed either on finite or semi-finite intervals [2,4,9,10,11,13,14,15,17,18,19,20,21,22]. In [28], we have studied boundary value problems for the following linear stationary dispersive equations on bounded intervals subject to general boundary conditions at the endpoints of intervals: censee MDPI, Basel, Switzerland.

Notations and Auxiliary Facts i

Formulation of the Problem

Local Regular Solutions

Global Regular Solutions

Exponential Decay of Small Regular Solutions

Conclusions