Three types of self-similar blow-up for the fourth-order p-Laplacian equation with source
In: Journal of computational and applied mathematics, Jg. 223 (2009), Heft 1, S. 326-355
Online
academicJournal
- print, 37 ref
Self-similar blow-up behaviour for the fourth-order quasilinear p-Laplacian equation with source, ut=-(|uxx)xx + |uP-1 u in R x R+ were n> 0, p > 1. is studied. Using variational setting for p = n + I and branching techniques for p ≠ n + 1, finite and countable families of blow-up patterns of the self-similar form uS (x, t) =(T-t) - 1/p-1f (y), where y=x/(T-t)β, β = - p-(n+1) / 2 (n+2) (p-1), are described by an analytic-numerical approach. Three parameter ranges: p = n + I (regional), p > n + 1 (single point), and 1 < p < n + 1 (global blow-up) are studied. This blow-up model is motivated by the second-order reaction-diffusion counterpart ut =(|ux|n ux)x + uP (u≥0). that was studied in the middle of the 1980s, while first results on blow-up of solutions were established by Tsutsumi in 1972.
Titel: |
Three types of self-similar blow-up for the fourth-order p-Laplacian equation with source
|
---|---|
Autor/in / Beteiligte Person: | GALAKTIONOV, V. A |
Link: | |
Zeitschrift: | Journal of computational and applied mathematics, Jg. 223 (2009), Heft 1, S. 326-355 |
Veröffentlichung: | Kidlington: Elsevier, 2009 |
Medientyp: | academicJournal |
Umfang: | print, 37 ref |
ISSN: | 0377-0427 (print) |
Schlagwort: |
|
Sonstiges: |
|