Existence and regularity of source-type self-similar solutions for stable thin-film equations

  • Mohamed Majdoub

    Imam Abdulrahman Bin Faisal University, Dammam, Saudi Arabia
  • Slim Tayachi

    Université de Tunis El Manar, Tunisia
Existence and regularity of source-type self-similar solutions for stable thin-film equations cover
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Abstract

We investigate the existence and the boundary regularity of source-type self-similar solutions to the thin-film equation where and is the Dirac mass at the origin. It is known that the leading order expansion near the edge of the support coincides with that of a traveling-wave solution for the standard thin-film equation: . In this paper we sharpen this result, proving that the higher-order corrections are analytic with respect to three variables: the first one is just the {spatial} variable, whereas the second and the third (except for ) are irrational powers of it. It is known that this third variable does not appear for the thin-film equation without gravity.

Cite this article

Mohamed Majdoub, Slim Tayachi, Existence and regularity of source-type self-similar solutions for stable thin-film equations. Interfaces Free Bound. 24 (2022), no. 3, pp. 431–457

DOI 10.4171/IFB/479