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A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces
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Laister, R., Robinson, James C., Sierżęga, Mikolaj and Vidal-López, A. (2016) A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Annales de l'Institut Henri Poincare (C) Non Linear Analysis , 33 (6). pp. 1519-1538. doi:10.1016/j.anihpc.2015.06.005 ISSN 0294-1449.
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Official URL: http://dx.doi.org/10.1016/j.anihpc.2015.06.005
Abstract
We consider the scalar semilinear heat equation , where 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 for all non-negative initial data , when is a bounded domain with Dirichlet boundary conditions. For this holds if and only if ; and for if and only if , where . This shows for the first time that the model nonlinearity is truly the ‘boundary case’ when , but that this is not true for .
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | ||||||||
Publisher: | Elsevier Masson | ||||||||
ISSN: | 0294-1449 | ||||||||
Official Date: | November 2016 | ||||||||
Dates: |
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Volume: | 33 | ||||||||
Number: | 6 | ||||||||
Page Range: | pp. 1519-1538 | ||||||||
DOI: | 10.1016/j.anihpc.2015.06.005 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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