On the Asymptotic Behavior of Solutions to the (Generalized) Kadomtsev–Petviashvili–Burgers Equations
✍ Scribed by Luc Molinet
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 289 KB
- Volume
- 152
- Category
- Article
- ISSN
- 0022-0396
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📜 SIMILAR VOLUMES
This paper is concerned with traveling waves for the generalized Kadomtsev}Petviashvili equation (w y)31, t31, i.e. solutions of the form w(t, , y)"u( !ct, y). We study both, solutions periodic in x" !ct and solitary waves, which are decaying in x, and their interrelations. In particular, we prove
We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation, 2 for t → ∞ uniformly with respect to x > 0 where α = 0 1, 0 q t = q/ √ π e -q 2 , 1 q t = 1/2 √ π √ t e -q 2 2q √ t -1 + e -2q √ t .
Using self-similar solution technique and comparison method, we obtain the growth rate of blowup solution and observe that the boundary-layer phenomena occurs.