Exact Solutions of the Precursor Film Equation

DOI10.1007/s10958-018-3810-4zbMath1413.76023OpenAlexW2802262295MaRDI QIDQ4558356

V. B. Bazarova, Vladislav Vasil'evich Pukhnachev

Publication date: 21 November 2018

Published in: Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-018-3810-4

zbMATH Keywords

invariant manifoldLagrangian coordinatesgroup analysisprecursor film

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Lubrication theory (76D08) Capillarity (surface tension) for incompressible viscous fluids (76D45) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Invariance and symmetry properties for PDEs on manifolds (58J70)

Cites Work

• Evolution equations and Lagrangian coordinates
• The Stefan problem. Translated from the Russian by Marek Niezgódka and Anna Crowley
• General solutions to the 2D Liouville equation
• Removable singularities and non-uniqueness of solutions of a singular diffusion equation
• Motion of hypersurfaces and geometric equations
• Local transformations between some nonlinear diffusion equations
• Differential constraints and exact solutions of nonlinear diffusion equations
• A new result for the porous medium equation derived from the Ricci flow
• Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities
• Self-similar solutions of some nonlinear equations
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