Blow-up for a semilinear heat equation with moving nonlinear reaction
Date
2018-01-22
Authors
Ferreira, Raul
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the behavior of solutions of the semilinear problem
ut = uxx + (1 + (T - t)-α X{|x| < (T - t)1/2})up, x ∈ ℝ, t ∈ (0, T),
u(x, 0) = u0(x) ≥ 0, x ∈ ℝ,
with α > 0 and p > 0. We describe, in terms of the parameters when the solution is bounded and when it blows up. For blowing up solutions we find the blow-up rate and the blow-up set.
Description
Keywords
Semilinear parabolic equation, Blow-up, Asymptotic behaviour
Citation
Ferreira, R. (2018). Blow-up for a semilinear heat equation with moving nonlinear reaction. <i>Electronic Journal of Differential Equations, 2018</i>(32), pp. 1-11.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.