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Asymptotic Analysis - Volume 61, issue 2

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Price: EUR 420.00
ISSN 0921-7134 (P)
ISSN 1875-8576 (E)

Impact Factor 2024: 1.1

The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. 

Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.

Stochastic homogenization of quasilinear PDEs with a spatial degeneracy

Authors: Delarue, François | Rhodes, Rémi

Article Type: Research Article

Abstract: We investigate stochastic homogenization for some degenerate quasilinear parabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium. Assuming that this reference diffusion operator is ergodic, we can prove the homogenization property for the quasilinear PDEs, by means of the first-order approximation method. The (nonlinear) limit operator need not be nondegenerate. Concrete examples are provided.

Keywords: stochastic homogenization, parabolic PDE, nonlinear PDE, degenerate PDE, first-order approximation, ergodic operator

DOI: 10.3233/ASY-2008-0925

Citation: Asymptotic Analysis, vol. 61, no. 2, pp. 61-90, 2009

Price: EUR 27.50

The Vlasov–Poisson system with strong external magnetic field. Finite Larmor radius regime

Authors: Bostan, Mihai

Article Type: Research Article

Abstract: We study here the finite Larmor radius regime for the Vlasov–Poisson equations with strong external magnetic field. The derivation of the limit model follows by formal expansion in power series with respect to a small parameter. If we replace the particle distribution by the center distribution of the Larmor circles the limit of these densities satisfies a transport equation, whose velocity is given by the gyro-average of the electric field. We justify rigorously the convergence towards the above model and we investigate the well-posedness of it.

Keywords: Vlasov–Maxwell equations, finite Larmor radius regime, gyro-average

DOI: 10.3233/ASY-2008-0908

Citation: Asymptotic Analysis, vol. 61, no. 2, pp. 91-123, 2009

Price: EUR 27.50
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