Asymptotic Analysis - Volume 70, issue 3-4

Authors: Wang, Wei | Zheng, Sining

Article Type: Research Article

Abstract: This paper studies heat equations with weighted nonlinear absorptions of the form ut =uxx −Mf(x)u−p in (−1,1)×(0,T) subject to Dirichlet boundary conditions u(−1,t)=u(1,t)=1 and initial data ϕ(x). The asymptotic estimates to quenching time and set of solutions as M→+∞ is established by local energy estimates. It is obtained that the quenching time T~m/(p+1)·M−1 with m=(max x (f(x)/ϕp+1 (x)))−1 as M→+∞. It is shown also how the quenching set concentrates near the maximum points of f/ϕp+1 for large M.

Keywords: heat equations, quenching time, quenching set, asymptotic estimates, local energy estimates, weighted absorptions

DOI: 10.3233/ASY-2010-1006

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 125-139, 2010

Authors: Chacón Rebollo, Tomás | Gómez Mármol, Macarena | Sánchez Muñoz, Isabel

Article Type: Research Article

Abstract: In this work we justify the way to set the boundary conditions by certain numerical methods to solve convection–diffusion problems, in particular convection–diffusion problems that appear in turbulence models. To do it, we analyze the limit of convection–diffusion equations when the total flux is imposed in the inflow boundary, and Newmann boundary conditions are imposed in the remaining of the boundary. We prove that the solution converges in L2 to the solution of the pure convection problem, with Dirichlet boundary conditions in the inflow boundary, in both the steady and evolution problems. In addition, the convective derivatives also converge …in L2 , and the convective traces in the inflow and outflow boundaries converge in spaces of L2 kind. Show more

Keywords: singular limit, convection–diffusion equations, total-flux boundary conditions

DOI: 10.3233/ASY-2010-1008

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 141-154, 2010

Authors: Papanicolaou, Andrew

Article Type: Research Article

Abstract: We consider nonlinear filtering applications to target tracking based on a vector of multi-scaled models where some of the processes are rapidly mean reverting to their local equilibria. We focus attention on target tracking problems because multiple scaled models with fast mean-reversion (FMR) are a simple way to model latency in the response of tracking systems. The main results of this paper show that nonlinear filtering algorithms for multi-scale models with FMR states can be simplified significantly by exploiting the FMR structures, which leads to a simplified Baum–Welch recursion that is of reduced dimension. We implement the simplified algorithms with …numerical simulations and discuss their efficiency and robustness. Show more

Keywords: nonlinear filtering, tracking, fast mean reversion, Kramers–Smoluchowski

DOI: 10.3233/ASY-2010-1011

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 155-176, 2010

Authors: Freddi, Lorenzo | Murat, François | Paroni, Roberto

Article Type: Research Article

Abstract: The aim of the paper is twofold. First, starting from the three-dimensional theory of linear elasticity, we give a simple justification of Saint-Venant theory for beams with multi-connected cross-section by means of Γ-convergence. Second, we estimate the error between the three-dimensional problem and the limit problem.

Keywords: beams, Saint-Venant theory, dimension reduction, error estimate

DOI: 10.3233/ASY-2010-1013

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 177-197, 2010

Authors: Cacciapuoti, Claudio | Finco, Domenico

Article Type: Research Article

Abstract: We discuss the limit of small width for the Laplacian defined on a waveguide with Robin boundary conditions. Under suitable hypothesis on the scaling of the curvature, we prove the convergence of the Robin Laplacian to the Laplacian on the corresponding graph. We show that in the limit of small width of the waveguide the transverse modes are independent. The projections on each transverse mode generically give rise to decoupling between the edges of the graph while exceptionally a coupling can occur. The coupling takes place if there exists a resonance at the threshold of the continuum spectrum of the …effective Hamiltonian resulting from the projection. Show more

Keywords: asymptotic dynamics of quantum systems, quantum graphs, constrained dynamics, Schrödinger operators

DOI: 10.3233/ASY-2010-1014

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 199-230, 2010

Authors: Kirwin, William D.

Article Type: Research Article

Abstract: We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the integrand. Our most general result assumes no smoothness of the functions of the integrand, but the expressions we obtain contain integrals which may be difficult to evaluate in practice. We then discuss additional assumptions which are sufficient to simplify these integrals, and for the common case that the functions in the integrand admit (finite) Taylor series and the exponent has a nondegenerate minimum, …we evaluate the integrals to obtain explicit formulae for the coefficients. Show more

Keywords: Laplace's approximation, Laplace integral, asymptotic expansion, series inversion

DOI: 10.3233/ASY-2010-1016

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 231-248, 2010

Article Type: Other

Citation: Asymptotic Analysis, vol. 70, no. 3-4, pp. 249-250, 2010