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Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics
Date
2020-01-01
Author
Kitavtsev, Georgy
Taranets, Roman M.
Metadata
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This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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In this paper, we extend the results of [8] by proving exponential asymptotic H-1-convergence of solutions to a one-dimensional singular heat equation with L-2-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.
Subject Keywords
Surfaces and Interfaces
URI
https://hdl.handle.net/11511/64786
Journal
INTERFACES AND FREE BOUNDARIES
DOI
https://doi.org/10.4171/ifb/437
Collections
Natural Sciences and Mathematics, Article