Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics

DOI10.4171/IFB/437zbMath1445.35063arXiv1810.02161OpenAlexW3038862248MaRDI QIDQ2194560

Roman M. Taranets, Georgy Kitavtsev

Publication date: 26 August 2020

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.02161

zbMATH Keywords

porous mediumsingular heatviscous liquid sheets

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Other free boundary flows; Hele-Shaw flows (76D27) Singular parabolic equations (35K67) Quasilinear parabolic equations (35K59)

Cites Work

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• Weak solutions to lubrication equations in the presence of strong slippage
• Asymptotic decay and non-rupture of viscous sheets
• Thermodynamically consistent models of phase-field type for the kinetics of phase transitions
• On a singular heat equation with dynamic boundary conditions
• Mathematical derivation of viscous shallow-water equations with zero surface tension
• A generalization of a lemma of bellman and its application to uniqueness problems of differential equations
• On the remarkable nonlinear diffusion equation (∂/∂x)[a (u+b)−2(∂u/∂x)−(∂u/∂t)=0]
• Shallow-Water Equations and Related Topics
• Singularities: Formation, Structure, and Propagation
• Some non-local transformations between nonlinear diffusion equations
• Heat Conduction in Simple Metals
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

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