Existence and blow-up of weak solutions for a sixth-order equation related to thin solid films

DOI10.1016/j.nonrwa.2010.05.008zbMath1203.35127OpenAlexW2070422525MaRDI QIDQ708586

Xiao-Chuan Liu, Chang-Zheng Qu

Publication date: 14 October 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.05.008

zbMATH Keywords

regularityexistenceuniquenessDirichlet boundary conditionsblow-upperiodic boundary conditionsblow-up timesixth-order equation

Mathematics Subject Classification ID

Initial-boundary value problems for higher-order parabolic equations (35K35) Thin fluid films (76A20) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

Related Items (5)

The Cauchy problem for a tenth-order thin film equation. I. bifurcation of oscillatory fundamental solutions ⋮ On the Rayleigh-Plateau instability ⋮ The Cauchy problem for a tenth-order thin film equation. II: Oscillatory source-type and fundamental similarity solutions ⋮ On the Rayleigh-Plateau instability. The regularity in H^3_per ⋮ Global Carleman estimate and its applications for a sixth-order equation related to thin solid films

Cites Work

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• Higher order nonlinear degenerate parabolic equations
• Higher order equations related to thin films: Blow-up and global existence, the influence of the initial data
• Two generalizations of the thin film equation
• The Isolation Oxidation of Silicon: The Reaction-Controlled Case
• Numerical and asymptotic solution of a sixth-order nonlinear diffusion equation and related coupled systems
• Unstable sixth-order thin film equation: I. Blow-up similarity solutions

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