DYNAMICAL INTERFACE TRANSITION IN RAMIFIED MEDIA WITH DIFFUSION

We consider interaction problems in ramified spaces of a rather genera l type with a distinguished interface transition in form of a dynamica l Kirchhoff condition. These conditions stem from applications and mod elling in biology and physics, see for instance [8, 21]. In the presen t paper our principal concern is to derive existence results in the li near and semilinear case and some qualitative principles similar to th e classical ones for initial boundary value problems on domains. Moreo ver, the influence of the dynamical interface condition on the solutio n is studied in the autonomous reaction-diffusion case.