QUENCHING FOR DEGENERATE PARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

TitleQUENCHING FOR DEGENERATE PARABOLIC PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS
Publication TypeJournal Article
Year of Publication2009
AuthorsCHAN C.Y, LIU H.T
JournalDynamic Systems and Applications
Volume18
Start Page17
Pagination12
Date Published2009
ISSN1056-2176
AMS Subject Classification35K20, 35K55, 35K57, 35K60, 35K65
Abstract

Let q be a nonnegative real number, and a and T be positive constants. This article studies the following degenerate parabolic problem: x qut − uxx = G(u) in (0, a) × (0, T], where G is a nonnegative function in the form of either f(u(x, t)), or Ra 0 h(x, t) f(u(x, t))dx for some positive, bounded and continuous function h with f > 0, f 0> 0, f 00≥ 0, and limu→1− f(u) = ∞. It is subject to the initial condition, u(x, 0) = 0 on [0, a], and the boundary conditions, u(0, t) = Za 0 M(x)|u (x, t)| p dx, u (a, t) = Za 0 N (x)|u (x, t)| r dx, t > 0, where p and r are constants greater than or equal to 1, and M and N are given nonnegative functions. Existence, uniqueness and criteria for quenching and non-quenching are studied.

PDFhttps://acadsol.eu/dsa/articles/18/02-DSA-CY-2-ChanLiu.pdf
Refereed DesignationRefereed