Name
Abstract | ||
|---|---|---|
We study the asymptotic behavior of classes of global and blow-up solutions of a semilinear parabolic equation of the "limit" Cahn-Hilliard type u(t) = -Delta(Delta u + | u|(p-1)u) in R-N x R+, p> 1, with bounded integrable initial data. We show that in some {p, N}-parameter ranges it admits a countable set of blow-up similarity patterns. The most interesting set of blow-up solutions is constructed at the first critical exponent p = p(0) = 1+2/N N, where the first simplest pro. le is shown to be stable. Unlike the blow-up case, we show that, for p = p(0), the set of global decaying source-type similarity solutions is continuous and determine the stable mass-branch. We prove that there exists a countable spectrum of critical exponents {p = p(l) = 1+ 2/ N+l, l = 0, 1, 2,...} creating bifurcation branches, which play a key role in general description of solutions globally decaying as t--> infinity. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/S0036141004440289 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
semilinear parabolic equation,similarity solutions,blow-up,asymptotic behavior | Countable set,Mathematical analysis,Cahn–Hilliard equation,Similarity solution,Asymptotic analysis,Critical exponent,Mathematics,Bounded function,Parabola | Journal |
Volume | Issue | ISSN |
38 | 1 | 0036-1410 |
Citations | PageRank | References |
2 | 0.47 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| J. D. Evans | 1 | 4 | 2.00 |
| V. A. Galaktionov | 2 | 23 | 5.25 |
| J. F. Williams | 3 | 38 | 4.79 |