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A free boundary problem of biological interest

✍ Scribed by Pierluigi Colli; Augusto Visintin; K. P. Hadeler

Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
557 KB
Volume
11
Category
Article
ISSN
0170-4214

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✦ Synopsis

Communicated by K. P. Hadeler

During fertilization of certain echinoderms, a long actin-filled tube is extended by the sperm towards the interior of the egg. This yields a parabolic free boundary problem, which differs from the classical one-phase Stefan problem by the presence of a convective term in the partial dilTerential equation, and because the equilibrium interface condition 8(s(t), t)=O is here replaced by a kinetic law s'(t)=vO(s(t),t). This problem is set in variational form and the existence of a solution is proved by means of a Faedo-Galerkin approximation procedure.

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## Abstract Let Ξ©~__i__~ βŠ‚ ℝ^__N__^, __i__ = 0, 1, be two bounded separately star‐shaped domains such that \documentclass{article}\pagestyle{empty}\begin{document}$ \Omega \_0 \supset \bar \Omega \_1 $\end{document}. We consider the electrostatic potential __u__ defined in \documentclass{article}\p