Abstract
We study the asymptotic behaviour as t → T^{–}, near a finite blowup time T > 0, of decreasinginx solutions to the following semilinear heat equation with a nonlocal term:(Figure presented.) with Neumann boundary conditions and strictly decreasing initial function u_{0}(x) with zero mass. We prove sharp estimates for u(x, t) as t → T^{–}, revealing a nonuniform global blowup:(Figure presented.) uniformly on any compact set [δ, 1], δ ∈ (0, 1).
Original language  English 

Pages (fromto)  893  923 
Number of pages  31 
Journal  Proceedings of the Royal Society of Edinburgh Section A  Mathematics 
Volume  145 
Issue number  5 
Early online date  24 Aug 2015 
DOIs  
Publication status  Published  Oct 2015 
Keywords
 asymptotic behaviour
 global blowup
 integral constraint
 nonlocal parabolic equation
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Profiles

Chris Budd
 Department of Mathematical Sciences  Professor
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Probability Laboratory at Bath
 Centre for Doctoral Training in Decarbonisation of the Built Environment (dCarb)
 Centre for Mathematical Biology
 Institute for Mathematical Innovation (IMI)
Person: Research & Teaching