Mathematical theory for the Ginzburg-Landau approximation in semilinear pattern forming systems with time-periodic forcing applied to electro-convection in nematic liquid crystals
Mesure invariante pour le système d’équations stochastiques du modèle de competition avec diffusion spatiale
Minimizing convex functions by continuous descent methods.
Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers
We consider the multifractal analysis for Birkhoff averages of continuous potentials on a class of non-conformal repellers corresponding to the self-affine limit sets studied by Lalley and Gatzouras. A conditional variational principle is given for the Hausdorff dimension of the set of points for which the Birkhoff averages converge to a given value. This extends a result of Barral and Mensi to certain non-conformal maps with a measure dependent Lyapunov exponent.
Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion
This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case. Our...