Asymptotic Analysis - Volume 48, issue 3

Authors: Babadjian, Jean-François | Baía, Margarida

Article Type: Research Article

Abstract: Γ-convergence techniques are used to give a characterization of the behavior of a family of heterogeneous multiple scale integral functionals. Periodicity, standard growth conditions and nonconvexity are assumed whereas a stronger uniform continuity hypothesis with respect to the macroscopic variable, normally required in the existing literature, is avoided. An application to dimension reduction problems in reiterated homogenization of thin films is presented.

Keywords: integral functionals, periodicity, homogenization, Γ-convergence, quasiconvexity, equi-integrability, dimension reduction, thin films

Citation: Asymptotic Analysis, vol. 48, no. 3, pp. 173-218, 2006

Authors: Leonori, Tommaso | Petitta, Francesco

Article Type: Research Article

Abstract: In this paper we deal with the asymptotic behavior of solution for quasilinear parabolic equations with absorbing lower-order terms whose model is \[\cases{u_{t}-\Delta u+u|\nabla u|^{2}=f& \mbox{in} \varOmega \times(0,T),\cr\noalign{\vspace{3pt}}u(x,0)=u_{0}& \mbox{in} \varOmega ,}\] with L1 data that do not depend on time. The main result states that, under suitable assumptions, the solution of the parabolic problem converges to the stationary solution.

Keywords: asymptotic behavior, quasilinear parabolic equations, natural growth

Citation: Asymptotic Analysis, vol. 48, no. 3, pp. 219-233, 2006

Authors: Bourget, Alain

Article Type: Research Article

Abstract: In this paper we show that the zeros of Van Vleck polynomials satisfy the strong law of large numbers and the central limit theorem as their degrees get arbitrary large.

Keywords: Heine–Stieltjes equation, Van Vleck polynomial, law of large numbers, central limit theorem

Citation: Asymptotic Analysis, vol. 48, no. 3, pp. 235-242, 2006

Authors: Nagai, Hideo

Article Type: Research Article

Abstract: Risk-sensitive variational inequalities (QVIs) for optimal investment with general transaction costs are studied. The QVIs are derived to solve impulse control problems formulated for power utility maximization on infinite time horizon with general transaction costs. The QVI for such kind of problem is of “ergodic type” in which the pair (u,l) of a function u and a constant l is considered to be a solution. The constant determines the value maximizing the growth rate of expected power utility to the investor's total wealth. An optimal strategy is constructed from the function u. The difficulty in solving the QVI lies in …that its related stopping problem is of a multiplicative functional, which enforce us to comprehend how to treat the quadratic growth nonlinear term appearing in the QVI from analytical, or probabilistic view points. Indeed we cannot employ the methods based on monotonicity which were effective in classical cases and need to invent other scheme constructing a solution instead. Besides, we would note, in spite of the name of “ergodic type”, the underlying diffusion process of the relevant QVI is not ergodic and it may include different features from the one studied by M. Robin (SIAM J. Control Optim. 19 (1981), 333–358) in this regard as well. Show more

Citation: Asymptotic Analysis, vol. 48, no. 3, pp. 243-265, 2006