The generalized Korteweg–de Vries–Burgers equation in

✍ Scribed by Tomasz Dlotko

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 292 KB
• Volume: 74
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2010.08.043

✦ Synopsis

The generalized KdV-Burgers equation u t +(δu xx +g(u)) x -νu xx +γ u = f (x), δ, ν > 0, γ ≥ 0, is considered in this paper. Using the parabolic regularization technique we prove local and global solvability in H 2 (R) of the Cauchy problem for this equation. Several regularity properties of the approximations stay valid for solutions constructed in such a way. Next, for when γ > 0, we study the asymptotic behavior of the corresponding semigroup on H 2 (R), constructing the (H 2 (R), H 3 -(R)) global attractor.