We consider a multidimensional model for the combustion of compressible reacting fluids. The flow is governed by the Navier-Stokes in Eulerian coordinates and the chemical reaction is irreversible and is governed by the Arrhenius kinetics. The existence of globally defined weak solutions is established by using weak convergence methods, compactness and interpolation arguments in the spirit of F...

In this paper, we investigate the existence of Pareto and weak Pareto equilibria for multiobjective games without compactness. By employing an existence theorem of Pareto equilibria due to Yu and Yuan([10]), several existence theorems of Pareto and weak Pareto equilibria for the multiobjective games are established in a similar way to Flores-Bázan([4]).

Corrected version Nov.20: a confused slide on the functional interpretation of weak compactness as well as a slide stating a bound on Browder's theorem have been deleted as the latter has been superseded meanwhile: weak compactess can be bypassed resulting in a primitive recursive bound.

In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.

We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-TransueOrlicz space Mq (Ω, μ) with q > 2.

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Let E be an ideal of Lo over a σ-finite measure space (Ω,Σ, μ), and let (X, ‖ ·‖X) be a real Banach space. Let E(X) be a subspace of the space Lo(X) of μ-equivalence classes of all strongly Σ-measurable functions f : Ω −→ X and consisting of all those f ∈ Lo(X) for which the scalar function ‖f(·)‖X belongs to E. Let E(X)n stand for the order continuous dual of E(X). In this paper we characteriz...