Singular Solutions of Doubly Singular Parabolic Equations with Absorption
Date
2000-11-08
Authors
Qi, Yuanwei
Wang, Mingxin
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper we study a doubly singular parabolic equation with absorption,
u(t) = div(|∇um |p-2∇um) - uq
with m > 0, p > 1, m(p - 1) < 1, and q > 1. We give a complete classification of solutions, which we call singular, that are non-negative non-trivial, continuous in ℝⁿ x [0,∞) \ {(0,0)}, and satisfy u(x,0) = 0 for all x ≠ 0. Applications of similar but simpler equations show that these solutions are very important in the study of intermediate asymptotic behavior of general solutions.
Description
Keywords
Doubly singular parabolic equation, Absorption, Singular solutions
Citation
Qi, Y., & Wang, M. (2000). Singular solutions of doubly singular parabolic equations with absorption. <i>Electronic Journal of Differential Equations, 2000</i>(67), pp. 1-22.
Rights
Attribution 4.0 International