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A hyperbolic system and the cost of the null controllability for the Stokes system
(Computational and Applied Mathematics, 2015-12-31)
This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method, we show that the cost of driving the Stokes system to rest at time $T$ is of order $e^{C/T}$ ...
Finite time blow-up for the bosonic Nordheim equation
(Inventiones mathematicae, 2015-12-31)
The homogeneous bosonic Nordheim equation is a kinetic equation describing the dynamics of the distribution of particles in the space of moments for a homogeneous, weakly interacting, quantum gas of bosons. We show the ...
Parallelizing the Kolmogorov-Fokker-Planck Equation
(ESAIM M2AN: Mathematical Modelling and Numerical Analysis, 2015-12-31)
We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker-Planck equation describing the ...
Molien series and low-degree invariants for a natural action of $SO(3) \wr Z_2$
(Journal of Physics A: Mathematical and Theoretical, 2015-12-31)
We investigate the invariants of the 25-dimensional real representation of the group SO(3) ? Z2 given by the left and right actions of SO(3) on 5 5 matrices together with matrix transposition; the action on column vectors ...
Hard-type inequalities for $\Delta_{\lambda}$-Laplacians
(Complex Variables and Elliptic Equations, 2015-12-31)
We derive Hardy-type inequalities for a large class of sub-elliptic operators that belong to the class of (Formula presented.) -Laplacians and find explicit values for the constants involved. Our results generalize previous ...
Long time dynamics of a multidimensional nonlinear lattice with memory
(Discrete and Continuous Dynamical Systems - Series B, 2015-12-31)
This work is devoted to study the nature of vibrations arising in a multidimensional nonlinear periodic lattice structure with memory. We prove the existence of a global attractor. In the homogeneous case under a restriction ...
Control of a hysteresis model subject to random failures
(Lecture Notes in Electrical Engineering, 2015-12-31)
The note presents conditions to assure weak stability in the mean for a hysteresis Bouc-Wen model controlled by a proportional-integral controller subject to random failures. When a failure happens, the controller turns ...
Complexity and regularity of maximal energy domains for the wave equation with fixed initial data
(Discrete and Continuous Dynamical Systems- Series A, 2015-12-31)
We consider the homogeneous wave equation on a bounded open connected subset Ω of IRn. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L2-norm of the ...
On the well-posedness of mathematical models for multicomponent biofilms
(Mathematical Methods in the Applied Sciences, 2015-12-31)
Bacterial biofilms are microbial depositions on immersed surfaces. Their mathematical description leads to degenerate diffusion-reaction equations with two non-Fickian effects: (i) a porous medium equation like degeneracy ...
Numerical approximation schemes for multi-dimensional wave equations in asymmetric spaces
(Mathematics of Computation, 2015-12-31)
We develop finite difference numerical schemes for a model arising in multi-body structures, previously analyzed by H. Koch and E. Zuazua, constituted by two n-dimensional wave equations coupled with a (n - 1)- dimensional ...