Geodesic
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
Applications of Mathematics, Tome 57 (2012) no. 2, pp. 143-165.

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We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential operator, and a variational approach is used in a certain non-direct way.
DOI : 10.1007/s10492-012-0010-2
Classification : 35B32, 35J50, 35J57, 35J87, 35J88, 35K57, 47J20
Keywords: reaction-diffusion system; unilateral condition; variational inequality; local bifurcation; variational approach; spatial patterns 
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     title = {A variational approach to bifurcation in reaction-diffusion systems with {Signorini} type boundary conditions},
     journal = {Applications of Mathematics},
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Baltaev, Jamol I.; Kučera, Milan; Väth, Martin. A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions. Applications of Mathematics, Tome 57 (2012) no. 2, pp. 143-165. doi : 10.1007/s10492-012-0010-2. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0010-2/

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