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R. Jordan, D. Kinderlehrer, and F. Otto proposed the discrete-time approximation of the Fokker—Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional, and the Gibbs—Boltzmann entropy functional. In this paper we study the asymptotic...
We prove that for any given set function F which satisfies F(∪ A
) and F(A)=-∈fty if meas (A)=0 , there must exist a measurable function g so that F(A) = ess sup_ y ∈ A g(y) . Two proofs of this result are given. Then a Riesz representation theorem for ``linear''...
In the treatment of the risk-sensitive control problem, it is known that the criterion function may not have a finite value. The risk parameter cannot be arbitrary. Conditions have been presented by the authors in previous papers to guarantee the no breakdown. In the present article, we present...
We prove the existence of a solution for an elastic frictional, quasistatic, contact problem with a Signorini non-penetration condition and a local Coulomb friction law. The problem is formulated as a time-dependent variational problem and is solved by the aid of an established shifting...
We consider coupled PDE systems comprising of a hyperbolic and a parabolic-like equation with an interface on a portion of the boundary. These models are motivated by structural acoustic problems. A specific prototype consists of a wave equation defined on a three-dimensional bounded domain Ω...
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