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Incompressible limit of a fluid-particle interaction model

Hongli Wang, Jianwei Yang (2021)

Applications of Mathematics

The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.

Indefinite Quasilinear Neumann Problem on Unbounded Domains

J. Chabrowski (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.

Indices of Orlicz spaces and some applications

Alberto Fiorenza, Miroslav Krbec (1997)

Commentationes Mathematicae Universitatis Carolinae

We study connections between the Boyd indices in Orlicz spaces and the growth conditions frequently met in various applications, for instance, in the regularity theory of variational integrals with non-standard growth. We develop a truncation method for computation of the indices and we also give characterizations of them in terms of the growth exponents and of the Jensen means. Applications concern variational integrals and extrapolation of integral operators.

Indirect stabilization of locally coupled wave-type systems

Fatiha Alabau-Boussouira, Matthieu Léautaud (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...

Indirect stabilization of locally coupled wave-type systems

Fatiha Alabau-Boussouira, Matthieu Léautaud (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, whereas it is known that exponential stability does not...

Inégalité d'observabilité du type logarithmique et estimation de la fonction de coût des solutions des équations hyperboliques

Leila Ouksel (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Dans ce travail, nous donnons une estimation logarithmique des données de la solution u, d'un problème hyperbolique avec condition aux limites de type Neumann, par la trace de u restreinte à un ouvert du bord, pendant un temps suffisamment grand qui nous permet d'estimer la fonction de coût de ce problème.

Currently displaying 61 – 80 of 430