Release Time:2019-03-11  Hits:

Indexed by: Journal Article

Date of Publication: 2015-01-01

Journal: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Included Journals: Scopus

Volume: 22

Issue: 1

Page Number: 1-16

ISSN: 14928760

Abstract: This paper studies the Cauchy problem of a degenerate parabolic equation not in divergence form with weighted source u<inf>t</inf> = up   u + a(x)uq in ?n    (0, T), where p    1, q > 1, and the positive weight function a(x) is of the order |x|m with m > 0. In a previous paper of the authors [Critical exponents in a degenerate parabolic equation with weighted source, Applicable Analysis 92 (2013), 814-830], the the critical and the second critical exponents were determined as q<inf>c</inf> = p+1 and a?= (Formula presented) respectively. Now we continue to consider the life span for the blow-up solutions and the large time behavior for the global solutions in the subregion of the coexistence exponent region with q > p + 1 +(Formula presented) > q<inf>c</inf>, or equivalently, 0 < a?< N. Copyright ? 2015 Watam Press.