Subcritical Kuramoto–Sivashinsky-type equation on a half-line

Subcritical Nonlinear Pseudodifferential Equation of Sobolev Type on a Half–line

We study the initialboundary value problem for the complex pseudodifferential equation of Sobolev type on a half-line { ∂t u+λ |u|σ u+Ku = 0, x ∈ R+, t > 0, u(0,x) = u0 (x) , x ∈ R+, where 0 < σ < 1, λ ∈ C , Ku = 1 2πi ∫ i∞ −i∞ epxK(p)û(t, p)dp. the symbol K(p) is defined as K(p) = (−1)n+1p2n n ∏ j=1 (p2 −aj )−1, n ∈ N, Reaj > 0, j = 1,2...,n, θ (x). . The aim of this paper is to prove the glob...

Benjamin-Ono Equation on a Half-Line

Spatial Analyticity on the Global Attractor for the KuramotoSivashinsky Equation

For the Kuramoto Sivashinsky equation with L-periodic boundary conditions we show that the radius of space analyticity on the global attractor is lowersemicontinuous function at the stationary solutions, and thereby deduce the existence of a neighborhood in the global attractor of the set of all stationary solutions in which the radius of analyticity is independent of the bifurcation parameter ...

The derivative nonlinear Schrödinger equation on the half-line

We analyze the derivative nonlinear Schrödinger equation iqt + qxx = i ( |q|q ) x on the half-line using the Fokas method. Assuming that the solution q(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x, t dependence and is given in terms of the ...

The Generalized Korteweg-de Vries Equation on the Half Line

The initial-boundary value problem for the generalized Korteweg-de Vries equation on a half-line is studied by adapting the initial value techniques developed by Kenig, Ponce and Vega and Bourgain to the initial-boundary setting. The approach consists of replacing the initial-boundary problem by a forced initial value problem. The forcing is selected to satisfy the boundary condition by inverti...