Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows

DOI10.1088/1361-6544/aa6eb3zbMath1432.35111arXiv1609.03913OpenAlexW2519026134MaRDI QIDQ4978479

Serafim Kalliadasis, Michael Charles Dallaston, D. Tseluiko, Zhong Zheng, Marco Antonio Fontelos

Publication date: 11 August 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.03913

zbMATH Keywords

thin-film flowsself-similar behaviourfinite-time singularity formation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Thin fluid films (76A20) Degenerate parabolic equations (35K65) Analyticity in context of PDEs (35A20) Higher-order parabolic equations (35K25) Self-similar solutions to PDEs (35C06) Quasilinear parabolic equations (35K59)

Related Items (6)

Nonlinear dynamics of dewetting thin films ⋮ The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics ⋮ Dynamics of fixed-volume pinned films – dealing with a non-self-adjoint thin-film problem ⋮ Instability, rupture and fluctuations in thin liquid films: theory and computations ⋮ Healing capillary films ⋮ Regular and complex singularities of the generalized thin film equation in two dimensions

Uses Software

• AUTO
• AUTO-07P

Cites Work

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• Falling liquid films.
• Thin-film rupture for large slip
• On a class of similarity solutions of the porous media equation
• Thin liquid films on a slightly inclined heated plate
• Dynamics of three-dimensional thin film rupture
• Dewetting films: bifurcations and concentrations
• A homotopy continuation approach for analysing finite-time singularities in thin liquid films
• Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities
• Dynamics and stability of an annular electrolyte film
• Long-wave instabilities of heated falling films: two-dimensional theory of uniform layers
• Self-similar rupture of viscous thin films in the strong-slip regime
• Nanoscale Fluid Structure of Liquid-solid-vapour Contact Lines for a Wide Range of Contact Angles
• Cascade of structures in long-wavelength Marangoni instability
• Stability of self-similar solutions for van der Waals driven thin film rupture
• Similarity solutions for van der Waals rupture of a thin film on a solid substrate
• Rupture of thin viscous films by van der Waals forces: Evolution and self-similarity
• Long-wave instabilities and saturation in thin film equations
• SLIDING AND SPREADING OF THIN TWO-DIMENSIONAL DROPS
• Nonlinear rupture of free films
• On the motion of a small viscous droplet that wets a surface
• The lubrication approximation for thin viscous films: the moving contact line with a 'porous media' cut-off of van der Waals interactions
• On the breakup of viscous liquid threads
• Spontaneous rupture of thin liquid films due to thermocapillarity: A full-scale direct numerical simulation
• Introduction to Numerical Continuation Methods
• Blowup and dissipation in a critical-case unstable thin film equation
• The spreading of drops with intermolecular forces
• Symmetric Singularity Formation in Lubrication-Type Equations for Interface Motion
• Exponential Asymptotics for Thin Film Rupture
• Interfacial thin films rupture and self-similarity
• Singularities: Formation, Structure, and Propagation
• Finite time rupture for thin films under van der Waals forces
• Self-similar slip instability on interfaces with rate- and state-dependent friction
• B<scp>IOFLUID</scp> M<scp>ECHANICS IN</scp> F<scp>LEXIBLE</scp> T<scp>UBES</scp>

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