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

Collections

Natural Sciences and Mathematics, Article