JournalsifbVol. 22, No. 2pp. 157–174

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

  • Georgy Kitavtsev

    Middle East Technical University, Mersin, Turkey
  • Roman M. Taranets

    National Academy of Sciences of Ukraine, Sloviansk, Ukraine
Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics cover
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Abstract

In this paper, we extend the results of [8] by proving exponential asymptotic H1H^1-convergence of solutions to a one-dimensional singular heat equation with L2L^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.

Cite this article

Georgy Kitavtsev, Roman M. Taranets, Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics. Interfaces Free Bound. 22 (2020), no. 2, pp. 157–174

DOI 10.4171/IFB/437