scholarly journals The Large-Time Development of the Solution to an Initial-Boundary Value Problem for the Korteweg-De Vries Equation. II. Expansion Wave Solutions

2010 ◽  
Vol 63 (4) ◽  
pp. 573-588 ◽  
Author(s):  
J. A. Leach
Keyword(s):  
Boundary Value Problem ◽  
Large Time ◽  
Vries Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Development ◽  
Expansion Wave ◽  
Wave Solutions ◽  
Initial Boundary Value

scholarly journals Benjamin-Ono Equation on a Half-Line

2010 ◽  
Vol 2010 ◽  
pp. 1-38 ◽  
Author(s):  
Nakao Hayashi ◽  
Elena I. Kaikina
Keyword(s):  
Boundary Value Problem ◽  
Large Time ◽  
Boundary Value ◽  
Nonlinear Partial Differential Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Half Line ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Boundary Value ◽  
Time Existence

We consider the initial-boundary value problem for Benjamin-Ono equation on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.

scholarly journals Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

2013 ◽  
Vol 469 (2159) ◽  
pp. 20130341 ◽  
Author(s):  
Elena I. Kaikina
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Boundary Data ◽  
Schrodinger Equation ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Robin Boundary

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time.

scholarly journals On Initial-Boundary Value Problem on Semiaxis for Generalized Kawahara Equation

2019 ◽  
Vol 65 (4) ◽  
pp. 683-699
Author(s):  
A. V. Faminskii ◽  
E. V. Martynov
Keyword(s):  
Boundary Value Problem ◽  
Global Solution ◽  
Existence And Uniqueness ◽  
Large Time ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Kawahara Equation ◽  
Initial Boundary Value

In this paper, we consider initial-boundary value problem on semiaxis for generalized Kawahara equation with higher-order nonlinearity. We obtain the result on existence and uniqueness of the global solution. Also, if the equation contains the absorbing term vanishing at infinity, we prove that the solution decays at large time values.

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