Quenching behavior of solutions to heat equations with coupled boundary singularities
Release Time:2019-03-10 Hits:
Indexed by: Journal Article
Date of Publication: 2008-12-01
Journal: APPLIED MATHEMATICS AND COMPUTATION
Included Journals: Scopus、EI、SCIE
Volume: 206
Issue: 1
Page Number: 403-412
ISSN: 0096-3003
Key Words: Quenching; Non-simultaneous quenching; Quenching rate; Heat equation; Nonlinear boundary flux; Characteristic algebraic system
Abstract: This paper deals with finite time quenching for one-dimensional heat equations coupled via negative singular boundary sources in the more general product form of two component powers u(-p1) v(-q1) and u(-p2) v(-q2). Differently from the generally considered, there are two additional singular factors, namely, u(-p1) and v(-q2) for the boundary sources of u and v, respectively. We at first propose a criterion to distinguish simultaneous and non-simultaneous quenching, and then determine all possible blow-up rates in the model, three for simultaneous quenching and two for non-simultaneous quenching, under different nominations. This shows real contributions of the two additional singular factors to the quenching behavior of solutions. (c) 2008 Elsevier Inc. All rights reserved.