Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions
Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.
Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples
The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.
Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities
Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.
Remarks on Krasnoselskii bifurcation theorem
Risultati di regolarità, stabilità, instabilità e biforcazione per un problema a frontiera libera