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Some linear parabolic system in Besov spaces

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2008)

Banach Center Publications

We study the solvability in anisotropic Besov spaces B p , q σ / 2 , σ ( Ω T ) , σ ∈ ℝ₊, p,q ∈ (1,∞) of an initial-boundary value problem for the linear parabolic system which arises in the study of the compressible Navier-Stokes system with boundary slip conditions. The proof of existence of a unique solution in B p , q σ / 2 + 1 , σ + 2 ( Ω T ) is divided into three steps: 1° First the existence of solutions to the problem with vanishing initial conditions is proved by applying the Paley-Littlewood decomposition and some ideas of Triebel. All considerations...

Some mathematical problems arising in heterogeneous insular ecological models.

Sébastien Gaucel, Michel Langlais (2002)

RACSAM

En esta nota se analizan dos modelos matemáticos deterministas planteados en problemas ecológicos causados por la introducción de nuevas especies en ambientes insulares heterogéneos. En el primero desarrollamos un modelo epidemológico con transmisión indirecta del virus por medio del ambiente. En el segundo se introduce un modelo específico de depredador-presa que exhibe la extinción en tiempo finito de las especies. Ambos modelos involucran sistemas de ecuaciones en derivadas parciales con interesantes...

Some models of Cahn-Hilliard equations in nonisotropic media

Alain Miranville (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We derive in this article some models of Cahn-Hilliard equations in nonisotropic media. These models, based on constitutive equations introduced by Gurtin in [19], take the work of internal microforces and also the deformations of the material into account. We then study the existence and uniqueness of solutions and obtain the existence of finite dimensional attractors.

Some new oscillation criteria for second order elliptic equations with damping

Rong-Kun Zhuang, Zheng-an Yao (2005)

Annales Polonici Mathematici

Some new oscillation criteria are obtained for second order elliptic differential equations with damping ∑ i , j = 1 n D i [ A i j ( x ) D j y ] + ∑ i = 1 n b i ( x ) D i y + q ( x ) f ( y ) = 0 , x ∈ Ω, where Ω is an exterior domain in ℝⁿ. These criteria are different from most known ones in the sense that they are based on the information only on a sequence of subdomains of Ω ⊂ ℝⁿ, rather than on the whole exterior domain Ω. Our results are more natural in view of the Sturm Separation Theorem.

Some properties of two-scale convergence

Augusto Visintin (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We reformulate and extend G. Nguetseng’s notion of two-scale convergence by means of a variable transformation, and outline some of its properties. We approximate two-scale derivatives, and extend this convergence to spaces of differentiable functions. The two-scale limit of derivatives of bounded sequences in the Sobolev spaces W 1 , p ⁢ R N , L r ⁢ o ⁢ t 2 ⁢ R 3 3 , L d ⁢ i ⁢ v 2 ⁢ R 3 3 and W 2 , p ⁢ R N is then characterized. The two-scale limit behaviour of the potentials of a two-scale convergent sequence of irrotational fields is finally studied.

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