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Interfaces and Free Boundaries


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Volume 22, Issue 2, 2020, pp. 157–174
DOI: 10.4171/IFB/437

Published online: 2020-07-06

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

Georgy Kitavtsev[1] and Roman M. Taranets[2]

(1) Middle East Technical University, Mersin, Turkey
(2) National Academy of Sciences of Ukraine, Sloviansk, Ukraine

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.

Keywords: Singular heat, porous medium, viscous liquid sheets

Kitavtsev Georgy, Taranets Roman: Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics. Interfaces Free Bound. 22 (2020), 157-174. doi: 10.4171/IFB/437