Displaying similar documents to “Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets”

Oscillations and concentrations generated by 𝒜 -free mappings and weak lower semicontinuity of integral functionals

Irene Fonseca, Martin Kružík (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

DiPerna's and Majda's generalization of Young measures is used to describe oscillations and concentrations in sequences of maps { u k } k L p ( Ω ; m ) satisfying a linear differential constraint 𝒜 u k = 0 . Applications to sequential weak lower semicontinuity of integral functionals on 𝒜 -free sequences and to weak continuity of determinants are given. In particular, we state necessary and sufficient conditions for weak* convergence of det ϕ k * det ϕ in measures on the closure of Ω n if ϕ k ϕ in W 1 , n ( Ω ; n ) . This convergence holds, for...

Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems

Stephan Luckhaus, Yoshie Sugiyama (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

We consider the following reaction-diffusion equation: ( KS ) u t = · u m - u q - 1 v , x N , 0 < t < , 0 = Δ v - v + u , x N , 0 < t < , u ( x , 0 ) = u 0 ( x ) , x N , where N 1 , m > 1 , q max { m + 2 N , 2 } .
In [Sugiyama, Nonlinear Anal. 63 (2005) 1051–1062; Submitted; J. Differential Equations (in press)] it was shown that in the case of q max { m + 2 N , 2 } , the above problem (KS) is solvable globally in time for “small L N ( q - m ) 2 data”. Moreover, the decay of the solution (u,v)...

Weak solutions for elliptic systems with variable growth in Clifford analysis

Yongqiang Fu, Binlin Zhang (2013)

Czechoslovak Mathematical Journal

Similarity:

In this paper we consider the following Dirichlet problem for elliptic systems: D A ( x , u ( x ) , D u ( x ) ) ¯ = B ( x , u ( x ) , D u ( x ) ) , x Ω , u ( x ) = 0 , x Ω , where D is a Dirac operator in Euclidean space, u ( x ) is defined in a bounded Lipschitz domain Ω in n and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the...

External approximation of first order variational problems estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving W - 1 , p norms obtained by Nečas and on the general framework of -convergence theory.

-convergence of functionals on divergence-free fields

Nadia Ansini, Adriana Garroni (2007)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of -convergence. We prove that the -limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the -limit is also stable under volume constraint and various type of boundary conditions.