Non-regular Domains Research Articles

Existence and uniqueness results for parabolic equations with Robin type boundary conditions in a non-regular domain of [formula omitted

This paper is devoted to the analysis of the following two-space dimensional linear parabolic equation ∂tu-∂x12u-∂x22u=f, subject to Robin type conditions ∂x1u+βu=0, on the lateral boundary, where the coefficient β satisfies suitable non-degeneracy assumptions. The right-hand side f of the equation is taken in L2. The problem is set in a domain of the form t,x1∈R2:0<t<T,φ1(t)<x1<φ2(t)×]0,b[, where φ1 and φ2 are smooth functions. One of the main issues of this work is that the domain can possibly be non-regular, for instance, the singular case where φ1(0)=φ2(0) is allowed. For this purpose, the domain decomposition method is employed.

Partwise Cross-Parameterization via Nonregular Convex Hull Domains

In this paper, we propose a novel partwise framework for cross-parameterization between 3D mesh models. Unlike most existing methods that use regular parameterization domains, our framework uses nonregular approximation domains to build the cross-parameterization. Once the nonregular approximation domains are constructed for 3D models, different (and complex) input shapes are transformed into similar (and simple) shapes, thus facilitating the cross-parameterization process. Specifically, a novel nonregular domain, the convex hull, is adopted to build shape correspondence. We first construct convex hulls for each part of the segmented model, and then adopt our convex-hull cross-parameterization method to generate compatible meshes. Our method exploits properties of the convex hull, e.g., good approximation ability and linear convex representation for interior vertices. After building an initial cross-parameterization via convex-hull domains, we use compatible remeshing algorithms to achieve an accurate approximation of the target geometry and to ensure a complete surface matching. Experimental results show that the compatible meshes constructed are well suited for shape blending and other geometric applications.

An existence result for non-Newtonian fluids in non-regular domains

We show the existence of weak solutions to the steady system describing the motion of certain non-Newtonian fluids in non-regular domains. This generalizes previous results for Lipschitz continuous domains. In the proof we combine a localization of the Lipschitz truncation method with a domain decomposition theorem, which enables to extend results known for nice domains to John domains.

On the resolution of a parabolic equation in a nonregular domain of ℝ^3

In this work we give new results of existence , uniqueness and maximal regularity of a solution to a parabolic equation set in a nonregular domain Q with Cauchy-Dirichlet boundary conditions, where Q = � (t,x1) ∈ R 2 :0 <t < T;ϕ1(t) < x1 < ϕ2(t) � ×)0,b( ⊆ R 3 with some assumptions on the functions (ϕi)i=1,2. The right-hand side term of the equation is taken in L 2 (Q) . The method used is based on the approximation of the domain Q by a sequence of subdomains (Qn)n which can be transformed into regular domains . This work is an extension of the one space variable case studied in (12).

Higher order semi compact scheme to solve transient incompressible Navier-Stokes equations

A fourth order semi compact finite difference scheme has been developed to solve unsteady incompressible Navier-Stokes equations in stream function and vorticity formulation. The governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle non-regular domains. Two test problems are utilized to explore the efficiency of the scheme. It is found that the solutions obtained with the present scheme are in good agreement with the analytical results or with the existing results depending on the availability.

Applications holomorphes propres entre certains domaines bornés de ℂ n

In this Note, we developp a new technic to study the existence of proper holomorphic mappings between a strictly pseudoconvex domain and certain special non-regular domains in ℂ n. In particular, it can be applied in the case of the minimal ball and the Lie ball. We prove that self-proper holomorphic mappings between such domains are biholomorphic. Furthermore, we establish a necessary and sufficient condition to factorize a proper holomorphic mapping by automorphisms. Scaling method is applied for the first time in a singular points of the boundary of the domains.

LAMINAR CHANNEL FLOW WITH A BLOCKED BRANCH LINE-TRANSFORMATION OF A NONREGULAR DOMAIN INTO A RECTANGULAR DOMAIN

Consideration is given to laminar flow in a channel from which a blocked branch line emanates at right angles. The channel and the branch line constitute a solution domain that is nonregular with respect to computer codes structured to deal with domains that are rectangular. As an application of a technique devised by Patankar, the nonregular domain was transformed into a rectangular domain within which the fluid experiences a stepwise change of viscosity, taking on infinite viscosity in regions where flow is not to exist. Numerical solutions were obtained for parametric values of the channel Reynolds number and of the dimensionless length of the blocked branch line. The results showed that the greatest disturbance of the main flow by the presence of the branch line occurs at low Reynolds numbers, but that the recirculation bubble in the branch line is more vigorous at high Reynolds numbers. The pressure drop in the channel is diminished by the presence of the branch line. The extent of the diminution is ...

Laminar Channel Flow with a Blocked Branch Line-Transformation of a Nonregular Domain into a Rectangular Domain

Laminar Channel Flow with a Blocked Branch Line-Transformation of a Nonregular Domain into a Rectangular Domain

The Dirichlet problem for the minimal surface equation in non-regular domains

In this paper we study the Dirichlet problem for the minimal surface equation in a open set Ω without any assumption about the regularity of ϖΩ. We prove an existence theorem using only the pseudoconvexity of Ω.

A nontrivial locally trivial algebra

Let R be a commutative domain and Kits field of fractions. Auslander and Goldman [l] proved that if R is regular, the map 8: BY(R) -+ BY(K) of the Brauer groups which is induced by the inclusion R G K is injective. They also proved that for the nonregular domain R[X, Y]/(X2 + Y2) /3 is not injective. As suggested by Grothendieck in his second paper on the Brauer group [3] ,3 need not be injective even if R is normal: simply replace R[X, Y]/(X2 + Y2) by R[X, Y, 21/(X2 + Y2 + Z2) in the example of Auslander and Goldman [l]. We can therefore ask the following weaker question: Is the map /3’: BY(R) -+ I$, Br(R,), p running through Spec(R) injective ? In other words: if A is an Azumaya algebra over R such that A, is isomorphic to a matrix algebra M,(Rp) for every prime ideal p of R, is then A isomorphic to the endomorphism ring End,(P) of a faithfully projective R-module? It is not difficult to see that this is true for every normal ring with at most one singular maximal ideal. The purpose of this note is to construct a two dimensional normal affine algebra R (e.g., over the complex field) for which /I’ is not injective. The method used here was inspired by Bernice Auslander’s paper [5]. She has told me that she has discovered a mistake in her proof of Corollary 4.4; this explains the apparent contradiction between my example and her corollary.