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Supersolutions for a class of semilinear heat equations
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Robinson, James C. and Sierżęga, Mikołaj (2012) Supersolutions for a class of semilinear heat equations. Revista Matemática Complutense . doi:10.1007/s13163-012-0108-9 ISSN 1139-1138.
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Official URL: http://dx.doi.org/10.1007/s13163-012-0108-9
Abstract
A semilinear heat equation ut=Δu+f(u) with nonnegative measurable initial data is considered under the assumption that f is nonnegative and nondecreasing and Ω⊆Rn . A simple technique for proving existence and regularity based on the existence of supersolutions is presented, then a method of construction of local and global supersolutions is proposed. This approach is then applied to the model case f(s)=sp with initial data in Lq(Ω) , for which an extension of the monotonicity-based existence argument is offered for the critical case ( n(p−1)/2=q>1 ) in all dimensions. New sufficient conditions for the existence of local and global classical solutions are derived in the critical and subcritical ( n(p−1)/2q>1 ) range of parameters. Some possible generalisations of the method to a broader class of equations are discussed.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Revista Matemática Complutense | ||||
Publisher: | Springer Italia Srl | ||||
ISSN: | 1139-1138 | ||||
Official Date: | October 2012 | ||||
Dates: |
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DOI: | 10.1007/s13163-012-0108-9 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/G007470/1 (EPSRC) |
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