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• W2128840892 abstract "We consider an anisotropic diffusion equation of the form u t = ∇∇( D(x)u ) in two dimensions, which arises in various applications, including the modelling of wolf movement along seismic lines and the invasive spread of certain brain tumours along white matter neural fibre tracts. We consider a degenerate case, where the diffusion tensor D(x ) has a zero-eigenvalue for certain values of x . Based on a regularisation procedure and various pointwise and integral a priori estimates, we establish the global existence of very weak solutions to the degenerate limit problem. Moreover, we show that in the large time limit these solutions approach profiles that exhibit a Dirac-type mass concentration phenomenon on the boundary of the region in which diffusion is degenerate, which is quite surprising for a linear diffusion equation. The results are illustrated by numerical examples." @default.
• W2128840892 created "2016-06-24" @default.
• W2128840892 creator A5041353240 @default.
• W2128840892 creator A5050122860 @default.
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• W2128840892 date "2012-12-20" @default.
• W2128840892 modified "2023-09-30" @default.
• W2128840892 title "Anisotropic diffusion in oriented environments can lead to singularity formation" @default.
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• W2128840892 doi "https://doi.org/10.1017/s0956792512000447" @default.
• W2128840892 hasPublicationYear "2012" @default.
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