Advances in Differential Equations

On the stability of line-shock profiles for Kadomtsev-Petviashvili-Burgers equations

Bassam Kojok

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Abstract

We investigate the KP-Burgers flow in the background of the shock profile solution of the KdV-Burgers equation. We show that the KdV-Burgers shock profile is stable and asymptotically stable under the KPB-I flow with respect to small perturbations in some spaces close to the energy space.

Article information

Source
Adv. Differential Equations Volume 15, Number 1/2 (2010), 99-136.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854765

Mathematical Reviews number (MathSciNet)
MR2588391

Zentralblatt MATH identifier
1191.35233

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 42B35: Function spaces arising in harmonic analysis 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 37K40: Soliton theory, asymptotic behavior of solutions 37K45: Stability problems

Citation

Kojok, Bassam. On the stability of line-shock profiles for Kadomtsev-Petviashvili-Burgers equations. Adv. Differential Equations 15 (2010), no. 1/2, 99--136. https://projecteuclid.org/euclid.ade/1355854765.


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