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Regularity analysis for systems of reaction-diffusion equations

Thierry Goudon, Alexis Vasseur (2010)

Annales scientifiques de l'École Normale Supérieure

This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi’s method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere...

Resolution of the time dependent Pn equations by a Godunov type scheme having the diffusion limit

Patricia Cargo, Gérald Samba (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the Pn model to approximate the time dependent transport equation in one dimension of space. In a diffusive regime, the solution of this system is solution of a diffusion equation. We are looking for a numerical scheme having the diffusion limit property: in a diffusive regime, it has to give the solution of the limiting diffusion equation on a mesh at the diffusion scale. The numerical scheme proposed is an extension of the Godunov type scheme proposed by Gosse to solve the P1 model...

Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator

Bernard Helffer, Thierry Ramond (2000)

Journées équations aux dérivées partielles

We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit Λ ( h ) of the ground state energy of this operator. For Kac’s spin model, Λ ( h ) is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...

Some spectral properties of the streaming operator with general boundary conditions

Mohamed Boulanouar (2008)

Applications of Mathematics

This paper deals with the spectral study of the streaming operator with general boundary conditions defined by means of a boundary operator K . We study the positivity and the irreducibility of the generated semigroup proved in [M. Boulanouar, L’opérateur d’Advection: existence d’un C 0 -semi-groupe (I), Transp. Theory Stat. Phys. 31, 2002, 153–167], in the case ∥ K ∥ ≥ 1 . We also give some spectral properties of the streaming operator and we characterize the type of the generated semigroup in terms of the...

Theory of Dilute Binary Granular Gas Mixtures

D. Serero, S. H. Noskowicz, I. Goldhirsch (2010)

Mathematical Modelling of Natural Phenomena

A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical...

Transfer matrices and transport for Schrödinger operators

François Germinet, Alexander Kiselev, Serguei Tcheremchantsev (2004)

Annales de l’institut Fourier

We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential are provided....

Currently displaying 61 – 80 of 86