Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 1999; 36(4): 637-647

Printed December 1, 1999

Copyright © The Korean Mathematical Society.

Layer oscillations in a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition

YoonMee Ham

Kyonggi University

Abstract

In this paper, we consider a free boundary problem with Pushchino dynamics satisfying the Dirichlet boundary condition. We shall show the stationary solutions $(v^*(x), s^*)$ exist and the Hopf bifurcation occurs at a critical point $\tau$ when $s^* \in (1/3, 1)$.

Keywords: Dirichlet boundary condition, free boundary problem, Hopf bifurcation

MSC numbers: Primary 35R35, 35B32; Secondary 35B25, 35K22, 35K57, 58F14, 58F22