Flat fronts and stability for the porous medium equation

DOI10.1080/03605302.2016.1244207zbMath1386.35183arXiv1403.5811OpenAlexW1581971489MaRDI QIDQ2955376

Clemens Kienzler

Publication date: 25 January 2017

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5811

zbMATH Keywords

singular integralsporous medium equationflatnesstraveling wave frontGaussian estimatespaces of

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Degenerate parabolic equations (35K65) Traveling wave solutions (35C07)

Related Items (11)

Convergence to sharp traveling waves of solutions for Burgers-Fisher-KPP equations with degenerate diffusion ⋮ Asymptotics near extinction for nonlinear fast diffusion on a bounded domain ⋮ Invariant manifolds for the thin film equation ⋮ Flatness implies smoothness for solutions of the porous medium equation ⋮ Stability of receding traveling waves for a fourth order degenerate parabolic free boundary problem ⋮ The thin-film equation close to self-similarity ⋮ Second order elliptic operators in \(L^2\) with first order degeneration at the boundary and outward pointing drift ⋮ The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness ⋮ A well-posedness result for a system of cross-diffusion equations ⋮ Porous medium equation with a drift: free boundary regularity ⋮ Null-controllability of perturbed porous medium gas flow

Uses Software

• DLMF

Cites Work

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• Geometric flows with rough initial data
• Partial differential equations with non-Euclidean geometries
• Fundamental solutions for second order subelliptic operators
• Eventual \(C^{\infty}\)-regularity and concavity for flows in one- dimensional porous media
• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• All time \(C^\infty\)-regularity of the interface in degenerate diffusion: A geometric approach
• Regularity properties of flows through porous media: The interface
• Nonlinear analytic semiflows
• Interfaces with a corner point in one-dimensional porous medium flow
• Non-negative solutions of theo porous medium eqation
• Hölder estimates for nonlinear degenerate parabolic sytems.
• A selfsimilar solution to the focusing problem for the porous medium equation
• Weak Solutions of the Porous Medium Equation
• Extensions of Hardy spaces and their use in analysis
• Regularity of the free boundary for the porous medium equation
• A harnack inequality for parabolic differential equations
• Correetion to “A Harnack Inequality for Parabolic Differential Equations”
• Bounds for the fundamental solution of a parabolic equation
• Regularity Propeties of Flows Through Porous Media
• Well-posedness for the Navier-Stokes equations

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