Focusing of an elongated hole in porous medium flow

DOI10.1016/S0167-2789(01)00150-6zbMath0989.35082MaRDI QIDQ5942852

Sigurd B. Angenent, John S. Lowengrub, Santiago Betelú, D. G. Aronson

Publication date: 19 March 2002

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

formal asymptotic argumentsnumerical grid around the interface

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Degenerate parabolic equations (35K65) Theoretical approximation in context of PDEs (35A35) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50)

Related Items (13)

The focusing problem for the porous medium equation: experiment, simulation and analysis ⋮ Self-similar collapse of a circular cavity of a power-law liquid ⋮ Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties ⋮ Cauchy-Dirichlet problems for the porous medium equation ⋮ Local bounds of the gradient of weak solutions to the porous medium equation ⋮ Renormalization group analysis of nonlinear diffusion equations with time dependent coefficients and marginal perturbations ⋮ Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology ⋮ Non-axial self-similar hole filling for the porous medium equation ⋮ Towards optimal regularity for the fourth-order thin film equation in \(\mathbb R^N\): Graveleau-type focusing self-similarity ⋮ Nonlinear diffusion from a delocalized source: affine self-similarity, time reversal, and nonradial focusing geometries ⋮ Numerical Renormalization Group Algorithms for Self-Similar Asymptotics of Partial Differential Equations ⋮ Regular and complex singularities of the generalized thin film equation in two dimensions ⋮ Converging gravity currents of power-law fluid

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