Journal ArticleDOI
Diffusion from an instantaneous point source with a concentration-dependent coefficient
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This article is published in Quarterly Journal of Mechanics and Applied Mathematics.The article was published on 1959-01-01. It has received 326 citations till now. The article focuses on the topics: Diffusion (business) & Point source.read more
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Difference approximations to interface curves for nonlinear diffusion equations with absorption
Kenji Tomoeda,Tatsuyuki Nakaki +1 more
TL;DR: In this article, the authors consider nonlinear reaction-diffusion equations with extinction phenomena in finite time and propose difference approximations to interface curves, and prove the convergence to exact interface curves.
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Near field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case
TL;DR: This paper characterize the large time behavior in such scale, thus completing the results of [Gilding-Goncerzewicz-2007], which considered the porous medium equation in an exterior two-dimensional domain which excludes a hole.
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Sunspot and starspot lifetimes in a turbulent erosion model
TL;DR: In this paper, the disintegration of a magnetic flux tube by nonlinear diffusion was investigated and two physically motivated functional forms for the diffusion coefficient were proposed: an inverse power-law dependence and a step-function dependence on the magnetic field magnitude.
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Nonlinear diffusion and viral spread through the leaf of a plant
Maureen P. Edwards,Peter M. Waterhouse,María Jesús Munoz-Lopez,Robert S. Anderssen,Robert S. Anderssen +4 more
TL;DR: In this paper, the authors used Lie symmetry analysis to model the spatial-temporal spread of a virus through the leaf of a plant and showed how the solution can be derived using Lie symmetric analysis.
Exact sharp-fronted solutions for nonlinear diffusion on evolving domains
TL;DR: In this paper, the authors present exact sharp-fronted solutions to a model of degenerate nonlinear diffusion on a growing domain by identifying a series of transformations that converts the model of non-linear diffusion to the porous medium equation on a fixed domain, which admits known exact solutions.