Title | ON OCCURRENCE OF COMPLETE BLOW-UP OF THE SOLUTION FOR A DEGENERATE SEMILINEAR PARABOLIC PROBLEM WITH INSULATED BOUNDARY CONDITIONS |
Publication Type | Journal Article |
Year of Publication | 2015 |
Authors | DYAKEVICH NADEJDAE |
Journal | Dynamic Systems and Applications |
Volume | 24 |
Start Page | 83 |
Pagination | 14 |
Date Published | 2015 |
ISSN | 1056-2176 |
AMS Subject Classification | 35K57, 35K60, 35K65 |
Abstract | Let a, σ, p, q, r, and m be constants with a > 0, σ > 0, p ≥ 0, q ≥ 0, r > 1, and m > 0. This article studies the following degenerate semilinear parabolic initial-boundary value problem, ξ quτ − uξξ = ξ pu r for 0 < ξ < a, 0 < τ < σ, u(ξ, 0) = u0 (ξ) = m for 0 ≤ ξ ≤ a, uξ(0, τ) = 0 = uξ(a, τ) for τ > 0. We derive criteria for u to blow up in finite time, and estimate the blow-up rate. We show that the blow-up is regional if q > p; the blow-up is complete if q = p; and the blow-up cannot be complete if p > q. |
https://acadsol.eu/dsa/articles/24/06-dsa-83-96.pdf | |
Refereed Designation | Refereed |