Title
Sign-Changing Solutions Of A Quasilinear Heat Equation With A Source Term
Keywords
Asymptotic estimates; Compact support; Quasilinear heat equation; Self-similar; Sign-changing
Abstract
The Cauchy problem of a heat equation with a source term ψt = Δ(|ψ|m-1 ψ) + |ψ|γ-1 ψ in (0,∞) × Rn is considered, where γ > m > 1. We are interested in global solutions with Hölder continuity which satisfy the equation in the distribution sense, and with a fixed number of sign changes at any given time t > 0. Through detailed analysis of the self-similarity problem, we prove the existence of two type of such solutions, one with compact support and the other decays to zero as |x| → ∞ with an algebraic rate determined uniquely by n,m and γ. Our results extend previous study on positive self-similar solutions. Moreover, they demonstrate vital difference from the well-studied semi-linear case of m = 1.
Publication Date
7-1-2013
Publication Title
Discrete and Continuous Dynamical Systems - Series B
Volume
18
Issue
5
Number of Pages
1389-1414
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.3934/dcdsb.2013.18.1389
Copyright Status
Unknown
Socpus ID
84876907154 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84876907154
STARS Citation
Liu, Guirong and Qi, Yuanwei, "Sign-Changing Solutions Of A Quasilinear Heat Equation With A Source Term" (2013). Scopus Export 2010-2014. 7168.
https://stars.library.ucf.edu/scopus2010/7168