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

2020-01-01
Kitavtsev, Georgy
Taranets, Roman M.
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.

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, vol. 22, no. 2, pp. 157–174, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64786.