Linear stability of source-type similarity solutions of the thin film equation

DOI10.1016/S0893-9659(02)80012-XzbMath1016.76031MaRDI QIDQ1609520

Andrew J. Bernoff, Thomas P. Witelski

Publication date: 15 August 2002

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

orthogonal polynomialslinear stabilityspectrumeigenfunctionsnonlinear diffusionlubrication equationsimilarity variablescompactly-supported source-type self-similar solutionsgeneralized thin film equation

Mathematics Subject Classification ID

Thin fluid films (76A20) Lubrication theory (76D08) Dimensional analysis and similarity applied to problems in fluid mechanics (76M55) Interfacial stability and instability in hydrodynamic stability (76E17)

Related Items (16)

Stability and regularity of weak solutions for a generalized thin film equation ⋮ A spectral analysis of the nonlinear Schrödinger equation in the co-exploding frame ⋮ The Cox–Voinov law for traveling waves in the partial wetting regime* ⋮ Numerical investigation of the generalized lubrication equation ⋮ Buoyancy segregation suppresses viscous fingering in horizontal displacements in a porous layer ⋮ Invariant manifolds for the thin film equation ⋮ The stochastic thin-film equation: existence of nonnegative martingale solutions ⋮ Stability of receding traveling waves for a fourth order degenerate parabolic free boundary problem ⋮ Nonlinear diffusion from a delocalized source: affine self-similarity, time reversal, and nonradial focusing geometries ⋮ On singularity formation in a Hele-Shaw model ⋮ Self-similar gravity currents in porous media: Linear stability of the Barenblatt--Pattle solution revisited ⋮ Numerical investigations on self-similar solutions of the nonlinear diffusion equation ⋮ Pressure-dipole solutions of the thin-film equation ⋮ A dynamical systems approach for the contact-line singularity in thin-film flows ⋮ Well-Posedness and Self-Similar Asymptotics for a Thin-Film Equation ⋮ The Spectrum of a Family of Fourth-Order Nonlinear Diffusions Near the Global Attractor

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