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In this paper we present a numerical study of the hyperbolic model for convection-diffusion transport problems that has been recently proposed by the authors [16]. This model avoids the infinite speed paradox, inherent to the standard parabolic model and introduces a new parameter τ called relaxation time. This parameter plays the role of an “inertia” for the movement of the pollutant. The analysis...
If (Ω, Σ, µ) is a probability space and X a Banach space, a theorem concerning sequences of X-valued random elements which do not converge to zero is applied to show from a common point of view that the F-normed space $$ L_p (\mu ,X) $$ of all classes of X-valued random variables, as well as the p-normed space Lp(µ, X) of all X-valued p-integrable random variables with 0 < p < 1 and the...
A completely geometrical approach for the construction of locally uniformly rotund norms and the associated networks on a normed space X is presented. A new proof providing a quantitative estimate for a central theorem by M. Raja, A. Moltó and the authors is given with the only external use of Deville-Godefory-Zizler decomposition method.
Let Ω be a nonempty open subset of the k-dimensional euclidean space ℝk. In this paper we show that, if S is an ultradistribution in Ω, belonging to a class of Roumieu type stable under differential operators, then there is a family $$ f_\alpha ,\alpha \in _0^k $$ , of elements of $$ {\cal L}_{loc}^\infty (\Omega ) $$ such that S is represented in the form $$ \Sigma _{\alpha \in _0^k...
Although there is general agreement that efficiency of problem resolution is strongly related to the problem representation adopted, computer problem solvers have been traditionally designed to keep the same representation throughout the whole of the problem solving process. A system able to change representation whilst the actual problem solving process occurs has advantages over traditional ones,...
Cascales, Kąkol, Saxon proved [3] that in a large class $$ E \in \mathfrak{G} $$ of locally convex spaces (lcs) (containing ( LM)-spaces and ( DF)-spaces) for a lcs $$ \mathfrak{G} $$ the weak topology σ ( E,E′) of E has countable tightness iff its weak dual ( E′, σ( E′,E)) is K-analytic. Applying examples of Pol [9] (and Kunen [12]) one gets that there exist Banach spaces C( X) over a compact...
We prove several uniform $$ L^1 $$ -estimates on solutions of a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of degenerate type. They are uniform in the sense that they don’t depend on the coefficients, nor on the size of the spatial domain. The estimates concern the own solution or/and its spatial gradient. This paper extends...
We prove that for suitable evolution problems, the solution u(t) corresponding to some right hand side term f(t) in V′ (with V some Hilbert space), only satisfies the stabilization property $$ (f(t) \to f_\infty $$ in V′ implies that $$ u(t) \to u_\infty $$ , in V , when t → +∞, with $$ u_\infty $$ solution of the associated stationary problem) when the space V is taken strictly larger...
Let Ω be a nonempty open set of the k-dimensional euclidean space ℝk. In this paper, we show that if S is an ultradistribution in Ω, belonging to a class of Beurling type stable under differential operators, then S can be represented in the forma $$ \Sigma _{\alpha \in _0^k } D^\alpha f_\alpha $$ , where $$ f_\alpha $$ is a complex function defined in Ω which is Lebesgue measurable and essentially...
The purpose of this article is to build a class of the best linear unbiased estimators (BLUE) of the linear parametric functions, to prove some necessary and sufficient conditions for their existence and to derive them from the corresponding normal equations, when a family of multivariate growth curve models is considered. It is shown that the classical BLUE known for this family of models is the...
We study a nonlinear parametric problem driven by a p-Laplacian-like operator (which need not be homogeneous) and with a ( p - 1)-superlinear nonlinearity which satisfy weaker conditions than the Ambrosetti-Rabinowitz condition. Using critical point theory, we show that for every λ > 0, the nonlinear parametric problem has a nontrivial solution. Then, by strengthening the conditions on the operator...
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