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Applications of Mathematics

, Volume 57, Issue 2, pp 143–165 | Cite as

A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions

  • Jamol I. Baltaev
  • Milan Kučera
  • Martin Väth
Article

Abstract

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.

Keywords

reaction-diffusion system unilateral condition variational inequality local bifurcation variational approach spatial patterns 

MSC 2010

35B32 35K57 35J50 35J57 47J20 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2012

Authors and Affiliations

  • Jamol I. Baltaev
    • 1
  • Milan Kučera
    • 2
  • Martin Väth
    • 2
    • 3
  1. 1.Department of MathematicsUrgench State UniversityKhorezmUzbekistan
  2. 2.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrague 1Czech Republic
  3. 3.Dept. of Mathematics (WE1)Free University of BerlinBerlinGermany

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