global attractors of two dimensional micropolar fluid flows in some unbounded domains this paper is concerned with the existence and regularity of the global attractors of micropolar fluid flows in two dimensional unbounded domains in which the poincare inequality holds true based on an asymptotic compactness argument a l 2 global attractor is shown to exist if the stationary external vector field is in h 1 moreover if the external vector field is in l 2 then the l 2 global attractor becomes an h 1 global attractor

superlinear convergence estimates for a conjugate gradient method for the biharmonic equation the method of muskhelishvili for solving the biharmonic equation using conformal mapping is investigated in r h chan t k delillo and m a horn siam j sci comput 18 1997 pp 1571 1582 it was shown using the hankel structure that the linear system in n i muskhelishvili some basic problems of the mathematical theory of elasticity noordhoff groningen the netherlands is the discretization of the identity plus a compact operator and therefore the conjugate gradient method will converge superlinearly estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a holder class

on the boundary integral formulation of the plane theory of elasticity with applications analytical aspects abstract a formulation of the plane strain problem of the theory of elasticity in stresses for simply connected domains is carried out in terms of real functions within the frame of what is known as the boundary integral method special attention is devoted to the problem of determination of the arbitrary constants appearing in the solution in view of work in progress where numerical techniques are used relying on some mathematical results formulated in the appendix simple applications concerning the first and the second fundamental problems for the circle and for the ellipse are given which show the correctness of the formulation and the necessity of recurring to numerical techniques once the geometry of the problem or the type of boundary conditions deviates from being simple following parts of the present work are devoted to the numerical treatment of the obtained system of equations as well as to the theories of thermoelasticity and thermo electromagneto elasticity

approximation methods for the muskhelishvili equation on smooth curves we investigate the possibility of applying approximation methods to the famous muskhelishvili equation on a simple closed smooth curve since the corresponding integral operator is not invertible the initial equation has to be corrected in a special way it is shown that the spline galerkin spline collocation and spline qualocation methods for the corrected equation are stable and the corresponding approximate solutions converge to an exact solution of the muskhelishvili equation in appropriate norms numerical experiments confirm the effectiveness of the proposed methods

asymptotic smoothing effect of solutions of two dimensional micropolar fluid flows abstract this paper is concerned with the micropolar fluid flows in two dimensional bounded domains based on gronwall type inequalities it is proved that the l 2 global attractor and the h 2 global attractor are the same and thus established the asymptotic smoothing effect of solutions

a fast interface solver for the biharmonic dirichlet problem on polygonal domains in this paper we propose and analyze an efficient discretization scheme for the boundary reduction of the biharmonic dirichlet problem on convex polygonal domains we show that the biharmonic dirichlet problem can be reduced to the solution of a harmonic dirichlet problem and of an equation with a poincare steklov operator acting between subspaces of the trace spaces we then propose a mixed fe discretization by linear elements of this equation which admits efficient preconditioning and matrix compression resulting in the complexity log varepsilon 1 o n log qn here n is the number of degrees of freedom on the underlying boundary varepsilon 0 is an error reduction factor q 2 or q 3 for rectangular or polygonal boundaries respectively as a consequence an asymptotically optimal iterative interface solver for boundary reductions of the biharmonic dirichlet problem on convex polygonal domains is derived a numerical example confirms the theory

existence of h2 global attractors of two dimensional micropolar fluid flows abstract it is shown that a two dimensional micropolar fluid flow in a bounded domain admits a global attractor which is compact in the space h 2 3 and attracts sets of functions bounded in the norm of l 2 3

on stability of approximation methods for the muskhelishvili equation we study approximation methods for the muskhelishvili integral equations on curves with comer points and establish necessary and sufficient conditions for their stability

stability of efficient sets continuity of mobile polarities whenever for every x e d such that a x afi xo for i 1 2 n one hash x fi x for each i pareto optimization is also referred to as uecror multi objecfiue or multi criteria optimization multi objective maximization problems 0 1 have been nowadays extended to the situations where f is a mapping from x to a set y equipped with a transitive relation 2 this relation is frequently called a preference consider first the image a f d of the constraint d an element y of a is called 3 efficient up to indifference or in the broad sense if for every y e a y z y implies y 5 yo it is said to be strongly z eficient or efficient in the narrow sense if for each y e a y 2 y implies y y the two notions coincide for antisymmetric transitive relations we shall be primarily concerned with efficient points in the broad sense the set of efficient points of a with respect to 7 will be denoted by max a max z a and that of strongly efficient points by max a an element of y is called an efficient value of 0 1 if it is an efficient point of f d an element x0 of d is a solution of 0 1 if f xo is an efficient point of f d we shall use the latter s to denote the set of solutions of 0 1

numerical computation of muskhelishvili s integral equation in plane elasticity based on muskhelishvili s integral equation and the schwarz christoffel integral a numerical procedure is developed for solving the stress fields on plates with emphasis on the region around crack tips the difficulties in the numerical determination of accessory parameters in the schwarz christoffel transformation are overcome by separating the improper integral into two parts a finite form of integral in a continuous region which can be integrated exactly and a definite integral free of singularity which can easily be computed numerically furthermore the difficulties in the numerical computation of the kernel function in the boundary integral equation are resolved by finding the limit of the kernel function as the source point approaches the field point some numerical results of plane stress problems are provided to demonstrate the accuracy of this approach

derivation and analytical investigation of three direct boundary integral equations for the fundamental biharmonic problem we derive and investigate three families of direct boundary integral equations for the solution of the plane fundamental biharmonic boundary value problem these three families are fairly general so that they as special cases encompass various known and applied equations as demonstrated by giving many references to the literature we investigate the families by analytical means for a circular boundary curve where the radius is a parameter we find for all three combinations of equations i that the solution of the equations is non unique for one or more critical radius radii and ii that this lack of uniqueness can always be removed by combining the integral equations with a suitable combination of one or more supplementary condition s we conjecture how the results obtained can or cannot be generalized to other boundary curves through the concept logarithmic capacity a few published general results about uniqueness are compared with our findings

spline galerkin methods for the sherman lauricella equation on contours with corners spline galerkin approximation methods for the sherman lauricella integral equation on simple closed piecewise smooth contours are studied and necessary and sufficient conditions for their stability are obtained it is shown that the method under consideration is stable if and only if certain operators associated with the corner points of the contour are invertible numerical experiments demonstrate a good convergence of the spline galerkin methods and validate theoretical results moreover it is shown that if all corners of the contour have opening angles located in interval 0 1 pi 1 9 pi then the corresponding galerkin method based on splines of order 0 1 or 2 is always stable these results are in strong contrast with the behavior of the nystrom method which has a number of instability angles in the interval mentioned

mellin convolution operators in bessel potential spaces abstract mellin convolution equations acting in bessel potential spaces are considered the study is based upon two results the first one concerns the interaction of mellin convolutions and bessel potential operators bpos in contrast to the fourier convolutions bpos and mellin convolutions do not commute and we derive an explicit formula for the corresponding commutator in the case of mellin convolutions with meromorphic symbols these results are used in the lifting of the mellin convolution operators acting on bessel potential spaces up to operators on lebesgue spaces the operators arising belong to an algebra generated by mellin and fourier convolutions acting on l p spaces fredholm conditions and index formulae for such operators have been obtained earlier by one of the authors and are employed here the results of the present work have numerous applications in boundary value problems for partial differential equations in particular for equations in domains with angular points

stability results for ekeland s e variational principle and cone extremal solutions given x a banach space and f x a a proper lower semicontinuous function which is bounded from below the ekeland s e variational principle asserts the existence of a point xi in x which we call e extremal with respect to f which satisfies fu fxi e u xi for all u x u xi by using set convergence notions kuratowski painleve mosco bounded hausdorff and their epigraphical versions we study the semi continuity properties of the mapping which to f associates e ext f the set of such e extremal points the key for the geometrical understanding of such properties is to consider the equivalent phelps extremization principle which given a closed set d in x and a partial ordering with respect to a pointed cone associates the set of elements of d maximal with respect to this order direct or potential applications are given in various fields multicriteria optimization numerical algorithmic calculus of variations

on the stability of the nystrom method for the muskhelishvili equation on contours with corners the stability of the nystrom method for the muskhelishvili equation on piecewise smooth simple contours is studied it is shown that in the space l 2 the method is stable if and only if certain operators a j from an algebra of toeplitz operators are invertible the operators a j depend on the parameters of the equation considered on the opening angles j of the corner points j and on parameters of the approximation method mentioned numerical experiments show that there are opening angles where the operators a j are noninvertible therefore for contours with such corners the method under consideration is not stable otherwise the method is always stable numerical examples show an excellent convergence of the method

layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains the symbolic calculus of pseudodifferential operators of mellin type is applied to study layer potentials on a plane domain q whose boundary 9q is a curvilinear polygon a singularity type is a zero of the determinant of the matrix of symbols of the mellin operators and can be used to calculate the bad values of p for which the system is not fredholm on lp 9q using the method of layer potentials we study the singularity types of the system of elastostatics lu uau au vdivu 0 in a plane domain q whose boundary 9k2 is a curvilinear polygon here u 0 and u a oo when a oo the system is the stokes system of hydrostatics for the traction double layer potential we show that all singularity types in the strip 0 re z i lie in the interval 1 1 so that the system of integral equations is a fredholm operator of index 0 on lp aq for all p 2 p oo the explicit dependence of the singularity types on a and the interior angles 0 of aq is calculated the singularity type of each corner is independent of a if the corner is nonconvex introduction recently there has been considerable interest in using layer potentials to solve lp boundary value problems for elliptic operators and systems on a lipschitz domain q in r for the systems of elastostatics dkv and hydrostatics fkv dahlberg fabes kenig and verchota have used rellich type identities to prove that the double layer potential integral equations yield a fredholm operator of index 0 on l 2 q for p 2 only limited information is available on the boundary integral equations for general lipschitz domains in rn the general problem of the notion of symbol on the boundary of a general lipschitz domain is still very much open in this paper we treat a very special case a curvilinear polygonal domain in r in this 2 dimensional case a precise symbolic calculus of pseudodifferential operators of mellin type is available we show that certain double layer boundary integral equations yield operators which for all p 2 p 00 are received by the editors december 14 1988 1980 mathematics subject classification 1985 revision primary 35j25 45e05 research partially supported by the italian cnr 1990 american mathematical society 0002 9947 90 1 00 25 per page

on upper and lower bounds of higher order derivatives for solutions to the 2d micropolar fluid equations the present paper is concerned with asymptotic behaviours of the solutions to the micropolar fluid motion equations in r2 upper and lower bounds are derived for the l2 decay rates of higher order derivatives of solutions to the micropolar fluid flows the findings are mainly based on the basic estimates of the linearized micropolar fluid motion equations and generalized gronwall type argument

continuous convergence and preservation of convergences of sets abstract a systematic study of convergence of images of families of relation is undertaken structurally these are questions from the theory of continuous convergence

parametrized multicriteria optimization continuity and closedness of optimal multifunctions this paper studies continuity properties of the marginal multifunction and solution multifunction for optimization problems with respect to a preorder relation among others we present a number of results which are generalizations to multicriteria problems of theorems due to c berge w hogan t tanino and y sawaragi

compact nets filters and relations abstract the notion of compact filter is introduced and compared to related notions of compact nets and compact relations a characterization of compact nets is given in regular spaces several applications in optimization theory and nonlinear analysis are presented

stability of the nystrom method for the sherman lauricella equation the stability of the nystrom method for the sherman lauricella equation on piecewise smooth closed simple contour gamma is studied it is shown that in the space l 2 the method is stable if and only if certain operators associated with the corner points of gamma are invertible if gamma does not have corner points the method is always stable numerical experiments show the transformation of solutions when the unit circle is continuously transformed into the unit square and then into various rhombuses examples also show an excellent convergence of the method