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2. Reaction-diffusion systems: destabilizing effect of conditions given by inclusions II, Examples.

Creator:
Eisner, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
bifurcation, spatial patterns, reaction-diffusion system, mollification, and inclusions
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Reaction-diffusion systems: destabilizing effect of conditions given by inclusions.

Creator:
Eisner, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
bifurcation, spatial patterns, reaction-diffusion system, mollification, and inclusions
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Smooth bifurcation for a Signorini problem on a rectangle

Creator:
Eisner, Jan, Kučera, Milan, and Recke, Lutz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Signorini problem, smooth bifurcation, variational inequality, boundary obstacle, and Crandall-Rabinowitz type theorem
Language:
English
Description:
We study a parameter depending semilinear elliptic PDE on a rectangle with Signorini boundary conditions on a part of one edge and mixed (zero Dirichlet and Neumann) boundary conditions on the rest of the boundary. We describe smooth branches of smooth nontrivial solutions bifurcating from the trivial solution branch in eigenvalues of the linearized problem. In particular, the contact sets of these nontrivial solutions are intervals which change smoothly along the branch. The main tools of the proof are first a certain local equivalence of the unilateral BVP to a system consisting of a corresponding classical BVP and of two scalar equations (which determine the ends of the contact intervals), and secondly an application of the classical Crandall-Rabinowitz type local bifurcation techniques (scaling and application of the Implicit Function Theorem) to that system.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public