Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Reflected Backward Stochastic Differential Equation with Jumps and RCLL Obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left-hand limited obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.

Periodic orbits in complex Abel equation

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Hopf bifurcation of a delay differential equation with two delays

We consider a delay differential equation with two delays. The Hopf bifurcation of this equation is investigated together with the stability of the bifurcated periodic solution, its period and the bifurcation direction. Finally, three applications are given.

Large deviation for BSDE with subdifferential operator

In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle.

Dynamics of the third order Lyness' difference equation

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Estudio de las diferentes alternativas para mejorar la respuesta de los filtros BAW (Bulk Acoustic Wave) con topología en escalera

Los requisitos de los dispositivos empleados en los nuevos sistemas de telecomunicaciones son: unas avanzadas prestaciones, reducido tamaño y bajo coste. Actualmente, se utilizan filtros basados en la tecnología SAW para trabajar a frecuencias de microondas. Dado los inconvenientes que presentan dicho tipo de filtros, se pretende substituirlos por filtros basados en tecnología BAW. La topología en escalera es hasta el momento la más extendida para diseñar estos filtros.

The equation xpyq=zr and groups that act freely on Λ-trees

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Model analític de les característiques DC de transistors de doble porta

En aquest treball s’implementa un model analític de les característiques DC del MOSFET de doble porta (DG-MOSFET), basat en la solució de l’equació de Poisson i en la teoria de deriva-difussió[1]. El MOSFET de doble porta asimètric presenta una gran flexibilitat en el disseny de la tensió llindar i del corrent OFF. El model analític reprodueix les característiques DC del DG-MOSFET de canal llarg i és la base per construir models circuitals tipus SPICE.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.