Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass
Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass
We consider a hybrid, one-dimensional, linear system consisting in two flexible strings connected by a point mass. It is known that this system presents two interesting features. First, it is well posed in an asymmetric space in which solutions have one more degree of regularity to one side of the point mass. Second, that the spectral gap vanishes asymptotically. We prove that the first property is a consequence of the second one. We also consider a system in which the point mass is replaced...
Asymptotic analysis for vanishing acceleration in a thermoviscoelastic system.
Asymptotic analysis, in a thin multidomain, of minimizing maps with values in
Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots
In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.
Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain
We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains , s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of . We give an explicit construction of that limit problem.
Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films
We consider the formation of solid drops (“islands”) occurring in the growth of strained solid films. Beginning from a detailed model for the growth of an alloy film that incorporates the coupling between composition, elastic stress and the morphology of the free boundary, we develop an asymptotic description of the shape and compositional nonuniformity of small alloy islands grown at small deposition rates. A key feature of the analysis is a “thin domain” scaling in the island which enables recasting...
Asymptotic and numerical modelling of flows in fractured porous media
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale, so that we can asymptotically reduce them to immersed polygonal fault interfaces and the model finally consists in a coupling between...
Asymptotic behavior for a dissipative plate equation in with periodic coefficients.
Asymptotic behavior for a nonlinear viscoelastic problem with a velocity-dependent material density.
Asymptotic behavior of eigenfunctions and eigenfrequencies of oscillation boundary value problems of the linear theory of elastic mixtures.
Asymptotic behavior of solutions on a thin plastic plate.
Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature
Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...
Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term
This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state” problem, which are obtained...
Asymptotic behavior of the numerical solutions of time-delayed reaction diffusion equations with non-monotone reaction term
This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem, which are...
Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity
The asymptotic behaviour for of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...
Asymptotic behaviour for Schrödinger equations with a quadratic nonlinearity in one-space dimension.
Asymptotic behaviour of an elastic body with a surface having small stuck regions
Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity theory and regularity
We prove -regularity for the stresses in the Prandtl-Reuss-law. The proof runs via uniform estimates for the Norton-Hoff-approximation.
Asymptotic distribution of eigenelements of the basic two-dimensional boundary-contact problems of oscillation in classical and couple-stress theories of elasticity.