JournalsifbVol. 8, No. 1pp. 111–129

Lower bounds on waiting times for degenerate parabolic equations and systems

  • Günther Grün

    Universität Erlangen-Nünberg, Germany
  • Lorenzo Giacomelli

    Università di Roma La Sapienza, Italy
Lower bounds on waiting times for degenerate parabolic equations and systems cover
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Abstract

We extend the method of \cite{GuLoRo00} to obtain quantitative estimates of waiting times for free boundary problems associated with degenerate parabolic equations and systems. Our approach is multi-dimensional, it applies to a large class of equations, including thin-film equations, (doubly) degenerate equations of second and of higher order and also systems of semiconductor equations. For these equations, we obtain lower bounds on waiting times which we expect to be optimal in terms of scaling. This assertion is true for the porous medium equation which seems to be the only PDE for which optimal quantitative estimates of the waiting time have been established so far (submitted for publication in {\it Interfaces and Free Boundaries}).

Cite this article

Günther Grün, Lorenzo Giacomelli, Lower bounds on waiting times for degenerate parabolic equations and systems. Interfaces Free Bound. 8 (2006), no. 1, pp. 111–129

DOI 10.4171/IFB/137