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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. (James Cooper), 1969- 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. 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
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of 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
Date:	1 January 2012
Volume:	Vol.385
Number:	No.1
Page Range:	pp. 105-110
Identification Number:	10.1016/j.jmaa.2011.06.023
Status:	Peer Reviewed
Publication Status:	Published
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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URI:	http://wrap.warwick.ac.uk/id/eprint/38735