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The goal of this paper is to study the fluid flow through a two-dimensional porous medium when we impose a leaky boundary condition. We show in particular that the situation is quite different from the one with the usual Dirichlet boundary condition.
This paper shows the property of weak lower semicontinuity of separately convex integrands under more general hypothesis than boundedness inL
2 of partial derivatives, and some properties of the parametrized measures associated with such sequences.
The set of attainable laws of the joint state-control process of a controlled diffusion is analyzed from a convex analytic viewpoint. Various equivalence relations depending on one-dimensional marginals thereof are defined on this set and the corresponding equivalence classes are studied.
We consider a nonlinear parabolic problem that models the evolution of a one-dimensional thermoelastic system that may come into contact with a rigid obstacle. The mathematical problem is reduced to solving a nonlocal heat equation with a nonlinear and nonlocal boundary condition. This boundary...
We define an anticipative stochastic integral with respect to a nonhomogeneous Wiener process in a dual of a nuclear space and investigate its basic properties. The theory is developed without the use of chaos expansions.
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