Korteweg-de Vries-Burgers equation on a segment

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DOI:

https://doi.org/10.4067/S0719-06462010000100005

Abstract

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 ∈ L2, then there exists a unique solution u ∈ C ([0, ∞) ; L2) ∪ C ((0,∞) ; H1) 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 → âˆž.

Keywords

Dissipative Nonlinear Evolution Equation , Large Time Asymptotics , Korteweg-de Vries-Burgers equation
  • Elena I. Kaikina Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, México.
  • Leonardo Guardado-Zavala Posgrado Eléctrica, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México.
  • Hector F. Ruiz-Paredes Posgrado Eléctrica, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México.
  • S. Juarez Zirate Posgrado Eléctrica, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México.
  • Pages: 41–58
  • Date Published: 2010-03-01
  • Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal

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Published

2010-03-01

How to Cite

[1]
E. I. Kaikina, L. Guardado-Zavala, H. F. Ruiz-Paredes, and S. Juarez Zirate, “Korteweg-de Vries-Burgers equation on a segment”, CUBO, vol. 12, no. 1, pp. 41–58, Mar. 2010.

Issue

Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal

Section

Articles