Asymptotic Analysis - Volume 5, issue 2

Authors: El Houakmi, Z. | Helffer, B.

Article Type: Research Article

Abstract: Soit P(h) un opérateur h-admissible sur Rn essentiellement autoadjoint, de symbole principal p0 . Soit I un intervalle de R et on suppose que le spectre de P(h) est purement ponctuel dans un voisinage de I. On suppose que l'opérateur commute avec l'action (linéaire) d'un groupe compact G. On donne dans cet article une estimation fine du comportement asymptotique, lorsque h→0, de la fonction de comptage des valeurs propres λρ j (h) de P(h) contenues dans I et correspondant à des vecteurs propres appartenant à un certain espace de représentation caractérisé par la donnée d'une représentation irréductible ρ de …G. Show more

DOI: 10.3233/ASY-1991-5201

Citation: Asymptotic Analysis, vol. 5, no. 2, pp. 91-113, 1991

Authors: Komornik, Vilmos

Article Type: Research Article

Abstract: We derive several new monotonicity properties and asymptotical formulae for the positive zeros of various Bessel type functions. Using these results we characterize the exactly controllable states for some circular plate models. We show that they are independent of the control time.

DOI: 10.3233/ASY-1991-5202

Citation: Asymptotic Analysis, vol. 5, no. 2, pp. 115-128, 1991

Authors: Duzaar, Frank | Fuchs, Martin

Article Type: Research Article

Abstract: Given a continuous mapping φ:M→N of compact manifolds we prove that there exists a differentiable solution of the problem Ep (u):=∫M |du|p dv$\leadsto$ Min in the homotopy class [φ] provided the sectional curvature of N is nonpositive. Here p∈[2,∞) is an arbitrary real number, hence we obtain an extension of a well-known theorem of Eells and Sampson. Our arguments are based on an asymptotic analysis of the less degenerate problems (0<ε<1) Ep ε (u):=∫M (ε+|du|2 )p/2 dv$\leadsto$ min in [φ] for which we establish the existence of solutions uε which converge to a minimizer of our original …variational problem. As further applications the paper contains various estimates for p-harmonic maps into negatively curved target manifolds. Show more

DOI: 10.3233/ASY-1991-5203

Citation: Asymptotic Analysis, vol. 5, no. 2, pp. 129-144, 1991

Authors: Ringeisen, E. | Sentis, R.

Article Type: Research Article

Abstract: We are concerned with the asymptotic behaviour of the linear transport equation ∂t u+ω▿u+(1/ε)Qu=0, u|t=0 =f, when ε→0. We prove that this process is equivalent up to order 1 to the viscosity perturbation of a hyperbolic process, provided that the conservative collision operator Q(x) has a 1-dimensional null-space. This can be considered as a justification of the diffusion approximation the classical scaling of the t or x variable.

DOI: 10.3233/ASY-1991-5204

Citation: Asymptotic Analysis, vol. 5, no. 2, pp. 145-159, 1991

Authors: Alber, Mark S.

Article Type: Research Article

Abstract: Geometric asymptotics in hyperbolic case are investigated. In particular, semiclassical solutions (modes) of the stationary Schrödinger equation corresponding to the Jacobi problem on geodesics on n-dimensional hyperboloids are constructed in the form of the multi-valued functions of several complex variables (geometric asymptotics) on the Jacobi varieties. Then a special limiting process (collapsing construction) is used in order to obtain from this problem reflected and diffracted modes for investigating geometric theory of diffraction.

DOI: 10.3233/ASY-1991-5205

Citation: Asymptotic Analysis, vol. 5, no. 2, pp. 161-172, 1991

Authors: Peng, Shige

Article Type: Research Article

Abstract: A new type of singularly perturbed stochastic differential equation is discussed. Its limit problem, which seems ill-posed, is proved to be well-posed under a certain reasonable condition. We show also how to apply the above result to treat a simulated annealing problem.

DOI: 10.3233/ASY-1991-5206

Citation: Asymptotic Analysis, vol. 5, no. 2, pp. 173-186, 1991