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.

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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

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Citation Formats

G. Kitavtsev and R. M. Taranets, “Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics,” INTERFACES AND FREE BOUNDARIES, pp. 157–174, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64786.