901 research outputs found
Stochastic porous media equations and self-organized criticality: convergence to the critical state in all dimensions
If is the solution to the stochastic porous media equation in
, modelling the self-organized
criticaity and is the critical state, then it is proved that
\int^\9_0m(\cal O\setminus\cal O^t_0)dt<\9, and
\lim_{t\to\9}\int_{\cal O}|X(t)-X_c|d\xi=\ell<\9,\ \mathbb{P}{-a.s.} Here,
is the Lebesgue measure and is the critical region
and a.e.
. If the stochastic Gaussian perturbation has only finitely many
modes (but is still function-valued), \lim_{t\to\9}\int_K|X(t)-X_c|d\xi=0
exponentially fast for all compact with probability one, if
the noise is sufficiently strong. We also recover that in the deterministic
case
Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case
We consider a possibly degenerate porous media type equation over all of
with , with monotone discontinuous coefficients with linear
growth and prove a probabilistic representation of its solution in terms of an
associated microscopic diffusion. This equation is motivated by some singular
behaviour arising in complex self-organized critical systems. The main idea
consists in approximating the equation by equations with monotone
non-degenerate coefficients and deriving some new analytical properties of the
solution
Boundary Controllability and Observability of a Viscoelastic String
In this paper we consider an integrodifferential system, which governs the vibration of a viscoelastic one-dimensional object. We assume that we can act on the system at the boundary and we prove that it is possible to control both the position and the velocity at every point of the body and at a certain time , large enough. We shall prove this result using moment theory and we shall prove that the solution of this problem leads to identify a Riesz sequence which solves controllability and observability. So, the result as presented here are constructive and can lead to simple numerical algorithms
Global Carleman inequalities for parabolic systems and applications to controllability
This paper has been conceived as an overview on the controllability properties of some relevant (linear and nonlinear) parabolic systems. Specifically, we deal with the null controllability and the exact controllability to the trajectories. We try to explain the role played by the observability
inequalities in this context and the need of global Carleman estimates. We also recall the main ideas used to overcome the difficulties motivated by nonlinearities. First, we considered the classical heat equation with Dirichlet conditions and distributed controls. Then we analyze recent extensions to
other linear and semilinear parabolic systems and/or boundary controls. Finally, we review the controllability properties for the Stokes and Navier–Stokes equations that are known to date. In this context, we have paid special attention to obtaining the necessary Carleman estimates. Some open questions are mentioned throughout the paper. We hope that this unified presentation will be useful for those researchers interested in the field.Ministerio de Educación y Cienci
Model selection for a semi - Markov continuous time regression observed in the discrete time moments
Malignant tumor with different localisation after klatskin tumor succesfully resected
Institutul Clinic Fundeni, Clinica Chirurgie Generală și Transplant Hepatic “Dan Setlacec”, Al XI-lea Congres al Asociației Chirurgilor „Nicolae Anestiadi” din Republica Moldova și cea de-a XXXIII-a Reuniune a Chirurgilor din Moldova „Iacomi-Răzeșu” 27-30 septembrie 2011Prezentare de caz: tumora Klatskin IIIb rezecată cu evoluția postoperatorie bună, diagnosticat la 3 ani cu tumoră gastrică.Case report: IIIb Klatskin tumor successfully resected with good postoperative outcome is diagnosed 3 years later with a gastric tumor
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