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

Socpus ID

84876907154 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84876907154

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