Young Measures on Topological Spaces

Castaing, Charles; Fitte, Paul Raynaud de; Valadier, Michel

doi:10.1007/1-4020-1964-5

Cited by 77 publications

(33 citation statements)

References 64 publications

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“…Remark 4.6. Let us also recall that since T N , B(T N ) is a countably generated σ-algebra then the topology Y (R N , X) is metrizable (see, for instance, the monograph of Castaing, Raynaud de Fitte, and Valadier [13]). …”

Section: Asymptotic Behaviormentioning

confidence: 99%

Asymptotic Behavior of a Nonlocal Diffusive Logistic Equation

Ducrot¹,

Magal²

2014

SIAM J. Math. Anal.

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Abstract. The long time behavior of a logistic-type equation modeling the motion of cells is investigated. The equation we consider takes into account birth and death processes using a simple logistic effect as well as a nonlocal motion of cells using a nonlocal Darcy's law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some information about its long time behavior. The lack of asymptotic compactness of the system is overcome by making use of the Young measure theory. This allows us to conclude that the semiflow converges for the Young measure topology.

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Section: Asymptotic Behaviormentioning

confidence: 99%

Asymptotic Behavior of a Nonlocal Diffusive Logistic Equation

Ducrot¹,

Magal²

2014

SIAM J. Math. Anal.

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“…Note that the restriction to L 0 (Ω; E) of the topology of stable convergence is the topology of convergence in probability. If (X n ) is a tight sequence in L 0 (Ω; E), then, by Prohorov's compactness criterion for Young measures [26,27], each subsequence of (X n ) has a further subsequence, say (X ′ n ), which converges stably to some µ ∈ Y(E), that is, for every A ∈ F and every f ∈ C b (E),…”

Section: Stable Convergence and Young Measuresmentioning

confidence: 99%

Existence of weak solutions to stochastic evolution inclusions

Jakubowski¹,

Kamenskii²,

Fitte³

2005

Comptes Rendus. Mathématique

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We prove the existence of a weak mild solution to the Cauchy problem for the semilinear stochastic differential inclusion in a Hilbert spacewhere W is a Wiener process, A is a linear operator which generates a C 0 -semigroup, F and G are multifunctions with convex compact values satisfying some growth condition and, with respect to the second variable, a condition weaker than the Lipschitz condition. The weak solution is constructed in the sense of Young measures.

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“…Our proof is different from those given in [4], the main difference concerns with the convergence of a new explicit projection algorithm to a solution of (1.1). The problem (1.1) is motivated by some applications in mathematical economics, mechanics, control theory and viscosity, see ( [2,3,10,9,11,12]). The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%