Arnold diffusion: a variational construction.
Xia, Zhihong (1998)
Documenta Mathematica
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Xia, Zhihong (1998)
Documenta Mathematica
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Jamol I. Baltaev, Milan Kučera, Martin Väth (2012)
Applications of Mathematics
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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...
Jan Eisner (2000)
Mathematica Bohemica
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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.
Marco Degiovanni, Antonio Marino (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We consider bifurcation problems associated with some lower semicontinuous functionals that do not satisfy the usual regularity assumptions. For such functionals it is possible to define a generalized "Hessian form" and to show that certain eigenvalues of this one are bifurcation values. The results are applied to a bifurcation problem for elliptic variational inequalities.
Marco Degiovanni, Antonio Marino (1987)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We consider bifurcation problems associated with some lower semicontinuous functionals that do not satisfy the usual regularity assumptions. For such functionals it is possible to define a generalized "Hessian form" and to show that certain eigenvalues of this one are bifurcation values. The results are applied to a bifurcation problem for elliptic variational inequalities.
Śladkowska, Janina (2015-11-13T13:54:55Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Jan Sokołowski (1987)
Banach Center Publications
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Xianqing Li-Jost (1995)
Manuscripta mathematica
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Jozef Kacur, Roger Van Keer (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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Degenerate parabolic variational inequalities with convection are solved by means of a combined relaxation method and method of characteristics. The mathematical problem is motivated by Richard's equation, modelling the unsaturated – saturated flow in porous media. By means of the relaxation method we control the degeneracy. The dominance of the convection is controlled by the method of characteristics.
Renate McLaughlin (1973)
Colloquium Mathematicae
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