Superdiffusive blow-up with advection
type: Item
instance of: scholarly article
title: Superdiffusive blow-up with advection
zbMATH Open document ID: 1252.35273
DOI: 10.1504/IJDSDE.2012.045997
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2012-11-16T00:00:00Z
review text: Summary: We examine the problem of a high-energy source localised within a superdiffusive medium with advection. This problem is modelled by a fractional diffusion equation with a nonlinear source term. Advection is introduced through a linear transport term that is proportional to the advection speed. In this paper we allow the medium to exhibit superdiffusive behaviour ranging from the classical (Gaussian) limit to the ballistic limit. We analyse the model to determine whether or not a thermal blow-up occurs. Specifically, it is shown that there exists a critical advection speed above which blow-up is avoided and below which blow-up is guaranteed. We also provide the asymptotic growth of the temperature near the time of blow-up.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35Q79
zbMATH DE Number: 6108265
zbMATH Keywords: superdiffusion
zbMATH Keywords: advection
zbMATH Keywords: thermal blow-up
zbMATH Keywords: nonlinear Volterra integral equations
author: C. M. Kirk
author: W. E. Olmstead
MaRDI profile type: Publication
full work available at URL: ijdsde.2012.045997
OpenAlex ID: W2043946260
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description: scientific article; zbMATH DE number 6108265