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arXiv · 1810.02161

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

Georgy Kitavtsev·Roman M. Taranets
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Abstract

In this paper, we extend the results of [1] 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.

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Georgy Kitavtsev, Roman M. Taranets. 2018-10-04. Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics. https://arxiv.org/abs/1810.02161

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