×

A Hopf bifurcation of interfaces in a Dirichlet problem. (English) Zbl 0936.35197

Summary: We consider a free boundary problem which is reduced from the propagator-controller system satisfying the Dirichlet boundary condition when a layer parameter is equal to zero. We show that the equilibria \((v^*(x), s^*)\) exist and there is a Hopf bifurcation at a critical point \(\tau\) only for \(s^*\in(\frac 13, 1)\).

MSC:

35R35 Free boundary problems for PDEs
35B32 Bifurcations in context of PDEs
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
35K57 Reaction-diffusion equations
PDF BibTeX XML Cite
Full Text: EuDML EMIS