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A note on well-posedness of semilinear reaction-diffusion problem with singular initial data
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Robinson, James C. and Sierżęga, Mikołaj (2012) A note on well-posedness of semilinear reaction-diffusion problem with singular initial data. Journal of Mathematical Analysis and Applications, Vol.385 (No.1). pp. 105-110. doi:10.1016/j.jmaa.2011.06.023 ISSN 0022247X.
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Official URL: http://dx.doi.org/10.1016/j.jmaa.2011.06.023
Abstract
We discuss conditions for well-posedness of the scalar reaction–diffusion equation ut=Δu+f(u) equipped with Dirichlet boundary conditions where the initial data is unbounded. Standard growth conditions are juxtaposed with the no-blow-up condition View the MathML source that guarantees global solutions for the related ODE View the MathML source. We investigate well-posedness of the toy PDE ut=f(u) in Lp under this no-blow-up condition. An example is given of a source term f and an initial condition ψ∈L2(0,1) such that View the MathML source and the toy PDE blows-up instantaneously while the reaction–diffusion equation is globally well-posed in L2(0,1).
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Reaction-diffusion equations | ||||
Journal or Publication Title: | Journal of Mathematical Analysis and Applications | ||||
Publisher: | Elsevier Science Ltd. | ||||
ISSN: | 0022247X | ||||
Official Date: | 1 January 2012 | ||||
Dates: |
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Volume: | Vol.385 | ||||
Number: | No.1 | ||||
Page Range: | pp. 105-110 | ||||
DOI: | 10.1016/j.jmaa.2011.06.023 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Date of first compliant deposit: | 18 December 2015 | ||||
Date of first compliant Open Access: | 18 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/G007470/1 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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