Dr Robert Laister Robert.Laister@uwe.ac.uk
Senior Lecturer
A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces
Laister, Robert; Robinson, James C.; Sierzega, Mikolaj; Vidal-Lopez, Alejandro
Authors
James C. Robinson
Mikolaj Sierzega
Alejandro Vidal-Lopez
Abstract
We consider the scalar semilinear heat equation ut−Δu=f(u), where f:[0,∞)→[0,∞) is continuous and non-decreasing but need not be convex. We completely characterise those functions f for which the equation has a local solution bounded in Lq(Ω) for all non-negative initial data u0∈Lq(Ω), when Ω⊂Rd is a bounded domain with Dirichlet boundary conditions. For q∈(1,∞) this holds if and only if limsups→∞s−(1+2q/d)f(s)
Journal Article Type | Article |
---|---|
Acceptance Date | Jun 25, 2015 |
Online Publication Date | Jul 26, 2015 |
Publication Date | Nov 1, 2016 |
Deposit Date | Jan 15, 2015 |
Publicly Available Date | Jul 26, 2016 |
Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
Print ISSN | 0294-1449 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 33 |
Issue | 6 |
Pages | 1519-1538 |
DOI | https://doi.org/10.1016/j.anihpc.2015.06.005 |
Keywords | Semilinear heat equation; Dirichlet problem; Local existence; Non-existence; Instantaneous blow-up; Dirichlet heat kernel |
Public URL | https://uwe-repository.worktribe.com/output/909531 |
Publisher URL | http://dx.doi.org/10.1016/j.anihpc.2015.06.005 |
Contract Date | May 22, 2016 |
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