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91.
We consider a Dirichlet problem in a planar domain with a hole of diameter proportional to a real parameter ? and we denote by u? the corresponding solution. The behavior of u? for ? small and positive can be described in terms of real analytic functions of two variables evaluated at (?,1/log??). We show that under suitable assumptions on the geometry and on the boundary data one can get rid of the logarithmic behavior displayed by u? for ? small and describe u? by real analytic functions of ?. Then it is natural to ask what happens when ? is negative. The case of boundary data depending on ? is also considered. The aim is to study real analytic families of harmonic functions which are not necessarily solutions of a particular boundary value problem. 相似文献
92.
Paolo Zanardo 《代数通讯》2015,43(1):158-173
Let R be a commutative ring and A be an R-module. The Mal'cev rank μ(A) of A is the sup of genN, where N ranges over the finitely generated submodules of A, and genN is the minimum number of generators of N. We prove that μ is both sub-additive and pre-additive as an invariant of Mod(R). Our main goal is to investigate μ for modules over pseudo-valuation domains. Specifically, we establish which pseudo-valuation domains R satisfy the property that an R-module of finite Mal'cev rank must be finitely generated. We split the class 𝒞 of pseudo-valuation domains as a union 𝒞 = 𝒞1 ∪ 𝒞2 ∪ 𝒞3 ∪ 𝒞4 of suitably defined subclasses, and prove that the property holds if and only if R ∈ 𝒞3 ∪ 𝒞4. In that case we can describe the R-modules A where μ(A) < ∞. We also show that, for R ∈ 𝒞4, there exist indecomposable R-modules of arbitrarily large finite Mal'cev rank. 相似文献
93.
In this paper we first show that the total energy of solutions for a semilinear system of elastic waves in Rn with a potential type of damping decays in an algebraic rate to zero. We study the critical potential case and we assume that the initial data have a compact support. An application for the Euler-Poisson-Darboux type dissipation V(t,x) is obtained and in this case the compactness of the support on the initial data is not necessary. Finally, we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain. 相似文献
94.
Liangliang DuXionghua Wu 《Applied mathematics and computation》2011,218(4):1379-1388
A rational differential quadrature method in irregular domains (RDQMID) is investigated to deal with a kind of singularly perturbed problems with boundary layers. Through a transformation, the boundary layer, which may be not straight, is transformed into a segment of a line parallel to one of the Cartesian axes. The rational differential quadrature method (RDQM) is applied to discretize the governing equation. Finally, a direct expansion method of the boundary conditions (DEMBC) is raised to deal with the boundary conditions. Numerical experiments show that RDQMID is of high accuracy, efficiency and easy to programme. 相似文献
95.
José M. Arrieta Marcone C. Pereira 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(15):5111-5132
In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations. 相似文献
96.
Micha Rzeczkowski 《Mathematische Nachrichten》2021,294(1):118-131
In the paper we prove that the Nevanlinna counting function and the Carleson function of analytic self‐maps of finitely connected domains with smooth boundary are equivalent. Using this result we obtain the characterization of compact composition operators on Hardy–Orlicz spaces. 相似文献
97.
Ge DONG 《数学年刊B辑(英文版)》2021,42(3):333-356
In this paper, the author studies the existence of the minimal nonnegative solutions of some elliptic variational inequalities in Orlicz-Sobolev spaces on bounded or unbounded domains. She gets some comparison results between different solutions as tools to pass to the limit in the problems and to show the existence of the minimal solutions of the variational inequalities on bounded domains or unbounded domains. In both cases,coercive and noncoercive operators are handled. The sufficient and necessary conditions for the existence of the minimal nonnegative solution of the noncoercive variational inequality on bounded domains are established. 相似文献
98.
In this paper we report synthesis of phase-pure highly resistive magnetoelectric BiFeO3 thin films on Pt/TiO2/SiO2/Si substrate by using pulsed laser deposition technique. For the first time saturated ferroelectric hysteresis loop has been
observed. It has confirmed the presence of ferroelectricity in BiFeO3 compound. The films exhibit dielectric anomaly near Neel temperature. This anomaly is related to the influence of vanishing
magnetic order on the electric order. In situ domain alignment occurs during observation of the films under transmission electron microscope. 相似文献
99.
D.P.A. Hardwick S.L. Naylor S. Bujkiewicz T.M. Fromhold D. Fowler A. Patan L. Eaves A.A. Krokhin P.B. Wilkinson M. Henini F.W. Sheard 《Physica E: Low-dimensional Systems and Nanostructures》2006,32(1-2):285
We study the effects of inter-miniband electron tunneling and electric field domains on the current–voltage and conductance–voltage curves of biased semiconductor superlattices under the action of a magnetic field that is tilted relative to the plane of the layers. For this geometry, electrons in the superlattice minibands exhibit a unique type of stochastic semiclassical motion. At certain critical values of the electric field within the superlattice layers, the stochastic trajectories change abruptly from fully localized to completely unbounded, and map out an intricate web-like mesh of conduction channels in phase space. Delocalization of the electron paths produces a series of strong resonant peaks in the electron drift velocity versus electric field curves. We use these drift velocity characteristics to make self-consistent drift-diffusion calculations of the current–voltage and differential conductance–voltage curves of the superlattices, which reveal strong resonant features originating from the sudden delocalization of the stochastic single-electron paths. We show that this delocalization has a pronounced effect on the distribution of space charge and electric field domains within the superlattices. Inter-miniband tunneling greatly reduces the amount of space-charge buildup, thus enhancing the domain structure and both the strength and number of the current resonances. 相似文献
100.
高进寿 《数学年刊A辑(中文版)》2006,(3)
设Ω是C~n中具有光滑边界的有限型m的凸域,本文的主要结果是把Gleason问题在加权Bergman空间的情形推广到Ω. 相似文献