Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics
| Autor: | Kitavtsev, Georgy, Taranets, Roman M. |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
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