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We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation on the interval (0, 1)We prove that if the initial data u0 ∈ L 2 , then there exists a unique solution u ∈ C [0, ∞) ; L 2 ∪ C (0, ∞) ; H 1 of the initial-boundary value problem (0.1). We also obtain the large time asymptotic of solution uniformly with respect to x ∈ (0, 1) as t → ∞. E.I. Kaikina et. al. CUBO 12, 1 (2010) RESUMENEstudiamos el siguiente problema de valor inicial en la frontera para la ecuación de Kortewegde Vries-Burgers en el intervalo (0, 1)Provamos que si el dato inicial u0 ∈ L 2 , entonces existe unaúnica solución u ∈ C [0, ∞) ; L 2 ∪ C (0, ∞) ; H 1 del problema de valor inicial en la frontera (0.1). También obtenemos comportamiento asintótico de la solución con respecto a x ∈ (0, 1) cuando t → ∞.

We study nonlinear Landau-Ginzburg-type equations on the half-line in the critical casewhere β ∈ C, ρ > 2. The linear operator K is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol K(p) = αp ρ , M = [ 1 2 ρ]. The aim of this paper is to prove the global existence of solutions to the initial-boundary-value problem and to find the main term of the asymptotic representation of solutions in the critical case, when the time decay of the nonlinearity has the same rate as that of the linear part of the equation.

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We study the equations governing the high-speed transmission in long-haul electrical systemsand F is the Fourier transformation. Our purpose in this paper is to obtain the large time asymptotics for the solutions under the nonzero mass condition ∫ 0 ( ) ̸ = 0.( ) the Fourier transform of the

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