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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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Cauchy-Dirichlet problems for the porous medium equation
TL;DR: In this article , the authors consider the porous medium equation subject to zero-Dirichlet conditions on a variety of two-dimensional domains, namely strips, slender domains and sectors, allowing them to capture a number of different classes of behaviours.
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Long-time asymptotics for the porous medium equation: The spectrum of the linearized operator
TL;DR: In this paper, the authors compute the complete spectrum of the displacement Hessian operator, which is obtained from the confined porous medium equation by linearization around its stationary attractor, the Barenblatt profile.
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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 D ∝ B −ν and a step-function dependence D on the magnetic field magnitude B.
Invariant Manifolds for the Thin Film Equation
Christian Seis,Dominik Winkler +1 more
TL;DR: In this article , the authors investigated the large-time behavior of solutions to the thin film equation with linear mobility in the complete wetting regime on RN and investigated the higher order asymptotics of solutions converging towards self-similar Smyth-Hill solutions under certain symmetry assumptions on the initial data.