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A semilinear heat equation with a localized nonlinear source and non‐continuous initial data
Author(s) -
Ferreira Lucas C. F.,
VillamizarRoa Elder J.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1490
Subject(s) - mathematics , bounded function , heat equation , domain (mathematical analysis) , nonlinear system , mathematical analysis , standard probability space , initial value problem , space (punctuation) , cauchy distribution , cauchy problem , lebesgue measure , lebesgue integration , physics , computer science , quantum mechanics , operating system
This paper is devoted to the study of the Cauchy problem for a semilinear heat equation with nonlinear term presenting a nonlinear source centered in a closed region of the spatial domain Ω. We assume that Ω ⊂ R nis either a smooth bounded domain or the whole spaceR n , n ≥ 2 . The initial datau 0is assumed to belong to the Lebesgue spaceL r( Ω ) . Copyright © 2011 John Wiley & Sons, Ltd.