Interfaces and Free Boundaries
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Published online: 2020-07-06
Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamicsGeorgy Kitavtsev and Roman M. Taranets (1) Middle East Technical University, Mersin, Turkey
(2) National Academy of Sciences of Ukraine, Sloviansk, Ukraine
In this paper, we extend the results of  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