Higher order equations related to thin films: Blow-up and global existence, the influence of the initial data

DOI10.1016/j.jde.2008.03.009zbMath1144.35025OpenAlexW2008990623MaRDI QIDQ925041

J. Emile Rakotoson, Cédric Verbeke, Jean Michel Rakotoson

Publication date: 29 May 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.03.009

zbMATH Keywords

Dirichlet boundary conditionssurface evolution

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Thin fluid films (76A20)

Related Items (5)

Existence and nonexistence of solutions of thin-film equations with variable exponent spaces ⋮ Localization, smoothness, and convergence to equilibrium for a thin film equation ⋮ A generalized thin-film equation in multidimensional space ⋮ The generalized thin film equation with periodic-domain conditions ⋮ Existence and blow-up of weak solutions for a sixth-order equation related to thin solid films

Cites Work

• Higher order nonlinear degenerate parabolic equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Two generalizations of the thin film equation
• Finite speed of propagation and continuity of the interface for thin viscous flows
• Finite-time blow-up of solutions of some long-wave unstable thin film equations
• An optimal compactness theorem and application to elliptic-parabolic systems
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