bluuebunny/crossref_metadata_2025_split huggingface dataset:
The steady state Navier–Stokes equations for incompressible flows with rotating boundaries
Authors: Sauer Niko 
Published: November 2011

SynopsisWhen a rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity field and the pressure field of the fluid motion and the angular velocity of the rigid body.In this paper we obtain existence and uniqueness results for the steady state problem in which a rigid body rotates about an axis of symmetry in a viscous incompressible fluid.
Output stabilisation for a class of linear parabolic differential equations
Authors: Nambu Takao 
Published: November 2011

SynopsisWe study the output stabilisation for a class of linear parabolic differential equations in a Hilbert space by means of feedback controls. The output is given as a finite number of linear functionals. Stabilisationof the state, of course, implies stabilisation of the output. In the present paper, however, we give a sufficient condition (an algebraic condition on the above functionals) for the output stabilisation, which is weakerin some sense than that for the state stabilisation.
Two perturbation results for nondegenerate solutions of some semilinear Dirichlet problems
Authors: Coclite Mario Michele 
Published: November 2011

SynopsisThe stability of nondegenerate solutions of some semilinear Dirichlet problems is studied. Two specific situations are considered: firstly, a singular perturbation of the differential operator; secondly, a perturbation of the nonlinear term using a term which also depends on the gradient of the solution.
Local minimisers and singular perturbations
Authors: Kohn Robert V. , Sternberg Peter 
Published: November 2011

SynopsisWe construct local minimisers to certain variational problems. The method is quite general and relies on the theory of Γ-convergence. The approach is demonstrated through the model problemIt is shown that in certain nonconvex domains Ω ⊂ ℝn and for ε small, there exist nonconstant local minimisers uε satisfying uε ≈ ± 1 except in a thin transition layer. The location of the layer is determined through the requirement that in the limit uε →u0, the hypersurface separating the states u0 = 1 and u0 = −1 locally minimises surface area. Generalisations are discussed with, for example, vector-valued u and “anisotropic” perturbations replacing |∇u|2.
Non-resonance for linear differential systems
Authors: Eastham M.S.P. , McLeod J.B. 
Published: November 2011

SynopsisThe existence of a set of real numbers σ, depending only on ∧0, is established such that if λ ∉ σ, the system Y'=(i∧0 + R)Y can be transformed into a system Z' = (i∧ + S)Z of the Levinson form. Here ∧0 and ∧ are real diagonal matrices, with ∧0 constant, and R(x) = ξ(x)T(λx). The scalar factor ξ(x) is o(l) (x →∞) and T belongs to a certain class of periodic matrices. The consequences for non-resonance, and the necessity of this class, are discussed.
Lifting homotopies through fixed points II
Authors: Armstrong M. A. 
Published: November 2011

SynopsisThis note complements an earlier paper of the same title. Let G be a discontinuous group of homeomorphisms of a connected, locally path connected, Hausdorff space X, and let ∏:X → X/G denote the associated projection. We work relative to a G-invariant subgroup H of the fundamental group of X and investigate the quotient group ∏1(X/G)/∏*(H). By choosing H appropriately, we can calculate ∏1(X/G) and show that ∏1(X/G)/∏*(∏1(X)) is isomorphic to G/F, where F is the normal subgroup of G generated by those elements which have fixed points. In a final section, we give analogous results for actions of a compact Lie group.
Integrable spreads
Authors: Farran H. R. , Robertson S. A. 
Published: November 2011

SynopsisFor any integer k such that 0≦k≦m, Mk denotes the Grassmann bundle of tangent k-planes on the m-manifold M. A k-spread on M is a field Φ of tangent k-planes on Mk such that the derivative of the projection maps Φ(λ) to λ. Previous work by Douglas and others studied the local properties of such spreads. Here we develop the global theory, with special emphasis on the case in which Φ is integrable.
Nonselfadjoint Schrödinger operators with singular first-order coefficients
Authors: Kato Tosio 
Published: November 2011

SynopsisSchrödinger operators of the form T = (i grad + b(x))2 + a(x) · grad + q(x) in Rm are considered, where a, b ate real vector-valued functions and q is a scalar complex-valued function. It is shown that T is essentially quasi-m-accretive in L2(Rm) if (1 + #x2223;∣)−1a ∈ L4 + L∞, div a ∈ L∞, , and Re q ≧ 0. The proof is elementary.
Double MS -algebras
Authors: Blyth T. S. , Varlet J. C. 
Published: November 2011

SynopsisWe introduce the notion of a double MS-algebra (L, 0, +) as an MS-algebra (L, 0) whose dual isan MS-algebra (Ld, +), with certain linking conditions concerning the operations x↦x0 and x↦x+. We determine necessary and sufficient conditions whereby an MS-algebra can be made into a double MS-algebra and show that this, when possible, can be done in one and only one way. We also consider the notion of a bistable subvariety of MS-algebras, namely a subvariety R with the property that, for every double MS-algebra (L, 0, +), whenever L, 0 ↦ R, we have (Ld,+)↦ R. Finally, we determine those subvarieties R of MS that are dense (in the sense that every MS-algebra L ↦ R can be made into a double MS-algebra), and those that are sparse (in the sense that if L ↦ R can be made into a double MS-algebra then it belongs to a proper subclass of R).
Asymptotic behaviour of solutions of some general nonlinear differential equations and integral inequalities
Authors: Beesack Paul R. 
Published: November 2011

SynopsisWe deal with the asymptotic behaviour, as t→∞, of complex-valued solutions of nonlinear differential equationsUpper bounds for ∣x(l)(t)∣, 0≦j≦n, are obtained by obtaining upper bounds for solutions u(t) of Bihari-type integral inequalities of the form
Fibrewise P-universal nilpotent fibrations
Authors: Scheerer H. 
Published: November 2011

SynopsisLet P be a set of primes. A nilpotent space X is called “P-universal”, if its P-localization canbe obtained as a direct limit over a sequence of selfmaps of X. A nilpotent fibration is called “fibrewiseP-universal”, if its fibrewise P-localization can be obtained in a similar way as a direct limit of fibrewise maps. In this paper, the following results are proved. Let π:E → B be a nilpotent fibration of connected finite or cofinite spaces. If π is fibrewise P-universal for some proper subset P of the set of primes, then its minimal model (in the sense of D. Sullivan's rational homotopy theory) admits a certaintype of weight decomposition. But the existence of such a weight decomposition implies only that there exists a finite set of primes, such that IT is fibrewise P-universal for all P with . In the absolute case however, i.e.B is a point, the set P can be chosen as the empty set. Thus a result announced by R. Body and D. Sullivan is recovered.
The form of blow-up for nonlinear parabolic equations
Authors: Lacey A. A. 
Published: November 2011

SynopsisSemilinear parabolic equations of the form u1 = ∇2u + δf(u), where f is positive and is finite, are known to exhibit the phenomenon of blow-up, i.e. for sufficiently large S, u becomes infinite after a finite time t*. We consider one-dimensional problems in the semi-infinite region x>0 and find the time to blow-up (t*). Also, the limiting behaviour of u as t→t*- and x→∞ is determined; in particular, it is seen that u blows up at infinity, i.e. for any given finite x, u is bounded as t→t*. The results are extended to problems with convection.The modified equation xu, = uxx +f(u) is discussed. This shows the possibility of blow-up at x =0 even if u(0, f) = 0. The manner of blow-up is estimated.Finally, bounds on the time to blow-up for problems in finite regions are obtained by comparing u with upper and lower solutions.
The theory of Legendrian unfoldings and first-order differential equations
Authors: Izumiya Shyuichi 
Published: November 2011

SynopsisWe consider some properties of completely integrable first-order differential equations for real-valued functions. In order to study this subject, we introduce the theory of Legendrian unfoldings. We give a characterisation of equations with classical complete solutions in terms of Legendrian unfoldings, and also assert that the set of equations with singular solutions is an open set in the space of completely integrable equations even though such a set is thin in the space of all equations.
Permanence in ecological systems with spatial heterogeneity
Authors: Cantrell Robert Stephen , Cosners Chris , Hutson Vivian 
Published: November 2011

SynopsisA basic problem in population dynamics is that of finding criteria for the long-term coexistence of interacting species. An important aspect of the problem is determining how coexistence is affected by spatial dispersal and environmental heterogeneity. The object of this paper is to study the problem of coexistence for two interacting species dispersing through a spatially heterogeneous region. We model the population dynamics of the species with a system of two reaction–diffusion equations which we interpret as a semi-dynamical system. We say that the system is permanent if any state with all components positive initially must ultimately enter and remain within a fixed set of positive states that are strictly bounded away from zero in each component. Our analysis produces conditions that can be interpreted in a natural way in terms of environmental conditions and parameters, by combining the dynamic idea of permanence with the static idea of studying geometric problems via eigenvalue estimation.
The existence of principal eigenvalues for problems with indefinite weight function on ℝk
Authors: Brown K. J. , Tertikas A. 
Published: November 2011

SynopsisWe investigate the existence of positive principal eigenvalues of the problem - ∆u(x) = λg(x)u(x) for x ∈ ℝk where the weight function g changes sign in ℝk and is negative for |x| sufficiently large.
A weighted norm inequality for the Hankel transformation
Authors: Heywood P. , Rooney P. G. 
Published: November 2011

SynopsisWe give conditions on pairs of non-negative weight functions U and V which are sufficient that for 1<p≤<∞where Hλ is the Hankel transformation.The technique of proof is a variant of Muckenhoupt's recent proof for the boundedness of the Fourier transformation between weighted Lp spaces, and we can also use this variant to prove a somewhat different boundedness theorem for the Fourier transformation.
The number of solutions to an equation from catalysis
Authors: Hastings S. P. , McLeod J. B. 
Published: November 2011

SynopsisIn catalysis theory there is interest in the number of solutions to the equationwith the boundary conditionsthe parameters λ,β, γ being all positive and p a non-negative integer. The paper answers this question when γ is large, which is the interesting situation physically. Although the treatment is somewhat different in the cases p = 0 and p ≠ 0, the final answer is the same, that is, given β, there exist two positive functions λ1(γ) and λ2(γ) such that the problem has one solution if λ<λ1(γ), or λ>λ2(γ), three solutions if λ1(γ)<λ <λ2(γ), and two solutions if λ=λ1(γ) or λ=λ2(γ).
Generic properties of equilibria of reaction-diffusion equations with variable diffusion
Authors: Rocha Carlos 
Published: November 2011

SynopsisIt is shown that, generically, scalar one-dimensional parabolic equations ut = (a2(x)ux)x + f(u), x ∈ [0, 1], with Neumann boundary conditions, have all the equilibrium solutions hyperbolic.Moreover, the bifurcations of these equilibria are generically of the saddle-node type.
Boundary value problems for systems of second order differential equations
Authors: Erbe L. H. , Knobloch H. W. 
Published: November 2011

SynopsisWe consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.
Uniform operator σ-additivity of indefinite integrals induced by scalar-type spectral operators
Authors: Okada S. , Ricker W. 
Published: November 2011

SynopsisThis note characterises those Banach space valued, scalar-type spectral operators T = ∫ z dP(z), where P is the resolution of the identity for T, whose indefinite spectral integral E→∫EzdP(z) as a set function of the Borel sets of the complex plane is countably additive with respect to the uniform operator topology.
Boundary integral equations for magnetic screens in ℝ3
Authors: Stephan Ernst P. 
Published: November 2011

SynopsisA boundary integral method is developed for the scattering of electromagnetic waves at thin obstacles. The exterior boundary value problem for the vector Helmholtz equation with given Neumann data on an open surface piece (screen S) is converted into a system of integral equations for the jumps of the tangential component of the field and its divergence across the screen. A slight modification of the Cauchy data yields a strongly elliptic system of pseudodifferential equations on S which can therefore be used for numerical computations using Galerkin's procedure. The resulting boundary integral equations are analysed using pseudodifferential operator calculus. The principal symbol concept, together with the Wiener–Hopf technique, are used to derive existence and regularity results for the solutions to the boundary integral equations. Quasi-optimal error estimates in the energy norm are given for the numerical scheme.
The G-invariant implicit function theorem in infinite dimensions II
Authors: Dancer E. N. 
Published: November 2011

SynopsisIn this paper, we study the perturbation of zeros of maps of Banach spaces where the maps are invariant under continuous groups of symmetries. In some cases, we allow the perturbed maps partially to break the symmetries. Our results improve earlier results of the author by removing smoothness conditions on the group action. The key new idea is a regularity theorem for the zeros of invariant Fredholm maps.
On Hamilton–Jacobi equations in bounded domains
Authors: Engler Hans 
Published: November 2011

SynopsisInitial-boundary value problems for nonlinear first order partial differential equations ∂tu + H(x, t, u, Dxu) = 0 and corresponding boundary value problems H(x, u, Dxu) = 0 are studied in bounded sets, using Crandal's and Lions' notion of viscosity solutions. We give pointwise conditions on the boundary data that guarantee the existence of such solutions and estimate their moduli of continuity in terms of continuity properties of the data. The results are applied to properties of the value function for certain differential games.
Strict inequalities for integrals of decreasingly rearranged functions
Authors: Friedman Avner , McLeod Bryce 
Published: November 2011

SynopsisIt is well known that iff,g,hare nonnegative functions andf*,g*,h* their symmetrically decreasing rearrangements, thenalso ifu* is a spherically decreasing rearrangement of a functionu,In this paper it is proved under suitable assumptions (including the assumption thathis already rearranged) that equality holds in (i) if and only iffandgare already rearranged, and, if 1 <p< ∞ equality holds in (ii) if and only ifuis already rearranged. We discuss (ii) both in ℝnand on the unit sphere.
Homoclinic and heteroclinic orbits of reversible vectorfields under perturbation
Authors: Churchill Richard C. , Rod David L. 
Published: November 2011

SynopsisAveraging techniques on Hamiltonian dynamical systems can often be used to establish the existence of hyperbolic periodic orbits. In equilibrium situations, it is then often difficult to show that there are homoclinic/heteroclinic connections between these hyperbolic orbits in the original unaveraged system. This existence problem is solved in this paper for a class of Hamiltonian systems admitting a sufficient number of symmetries (including reversing symmetries). Under isoenergetic reduction, the problem is reduced to one involving reversible vector fields under time-dependent perturbations admitting the same reversing symmetries. Applications are made to the one-parameter Hénon-Heiles family. The paper concludes with remarks on the problem of showing transversality of these homoclinic/heteroclinic orbits.
Hölder gradient estimates for fully nonlinear elliptic equations
Authors: Trudinger Neil S. 
Published: November 2011

SynopsisIn this paper we prove interior and global Hölder estimates for Lipschitz viscosity solutions of second order, nonlinear, uniformly elliptic equations. The smoothness hypotheses on the operators are more general than previously considered for classical solutions, so that our estimates are also new in this case and readily extend to embrace obstacle problems. In particular Isaac's equations of stochastic differential game theory constitute a special case of our results, and moreover our techniques, in combination with recent existence theorems of Ishii, lead to existence theorems for continuously differentiable viscosity solutions of the uniformly elliptic Isaac's equation.
On the instability of non-semi-Fredholm closed operators under compact perturbations with applications to ordinary differential operators
Authors: Labuschagne L. E. 
Published: November 2011

SynopsisThe stability of several natural subsets of the bounded non-semi-Fredholm operators undercompact perturbations were studied by R. Bouldin [2] in separable Hilbert spaces and by M. Gonzales and V. M. Onieva [6] in Banach spaces. The aim of this paper is to study this problem for closed operators in operator ranges. The main results are a characterisation of the non-semi-Fredholm operators with respect to α-closed and α-compact operators as well as a generalisation of a result of M. Goldman [5]. We also give some applications of the theory developed to ordinary differential operators.
Perturbation theory for dual semigroups II. Time-dependent perturbations in the sun-reflexive case
Authors: Clément Ph. , Diekmann O. , Gyllenberg M. , Heijmans H. J. A. M. , Thieme H. R. 
Published: November 2011

SynopsisWe consider time-dependent perturbations of generators of strongly continuous semigroups on a Banach space. The perturbations map the Banach space into a bigger space, which is the second dual of the original space in a specific semigroup sense. Using the theory of dual semigroups we show that the solutions of a generalised variation-of-constants formuladefine an evolutionary system. We investigate continuity and differentiability propertiesof this evolutionary system and its dual system and examine in what sense the perturbed generator and its adjoint generate these evolutionary systems. It is shown that the results apply naturally to retarded functional differential equations and age structured population dynamics.
Levinson's theorem and Titchmarsh-Weyl m(λ) theory for Dirac systems*
Authors: Hinton D. B. , Klaus M. , Shaw J. K. 
Published: November 2011

SynopsisA Levinson theorem is proved for a Dirac system with one singular endpoint. The number ofbound state is expressed in terms of the change in asymptotic phase of an appropriate solution and in terms of factors whose values depend on the presence of half-bound states. The behaviour of the asymptotic phase is used to determine the asymptotic behaviour of the Titchmarsh-Weyl m-function.
Regularity results for equilibria in a variational model for fracture
Authors: Acerbi Emilio , Fonseca Irene , Fusco Nicola 
Published: November 2011

SynopsisIn recent years models describing interactions between fracture and damage have been proposed in which the relaxed energy of the material is given by a functional involving bulk and interfacial terms, of the formwhere Ω is an open, bounded subset of ℝN, q ≧1, g ∈ L∞ (Ω ℝN), λ, β > 0, the bulk energy density F is quasiconvex, K⊂ℝN is closed, and the admissible deformation u:Ω→ ℝN is C1 in Ω\K One of the main issues has to do with regularity properties of the ‘crack site’ K for a minimising pair (K, u). In the scalar case, i.e. when uΩ→ ℝ, similar models were adopted to image segmentation problems, and the regularity of the ‘edge’ set K has been successfully resolved for a quite broad class of convex functions F with growth p > 1 at infinity. In turn, this regularity entails the existence of classical solutions. The methods thus used cannot be carried out to the vectorial case, except for a very restrictive class of integrands. In this paper we deal with a vector-valued case on the plane, obtaining regularity for minimisers of corresponding to polyconvex bulk energy densities of the formwhere the convex function h grows linearly at infinity.
Stochastic systems governed by B-evolutions on Hilbert spaces
Authors: Ahmed N. U. , Kerbal S. 
Published: November 2011

SynopsisIn this paper, we consider the question of existence of solutions and their regularity properties for a large class of stochastic evolution equations governed by B-evolutions involving two different Hilbert spaces. This allows dynamic boundary conditions together with noisy boundary data. They cover also stochastic boundary value problems. Our results are illustrated by two practical examples.
Positive solution curves of semipositone problems with concave nonlinearities
Authors: Castro Alfonso , Gadam Sudhasree , Shivaji R. 
Published: November 2011

SynopsisWe consider the positive solutions to the semilinear equation:where Ω denotes a smooth bounded region in ℝN(N> 1) and ℷ 0. Heref:[0, ∞)→ℝ is assumed to be monotonically increasing, concave and such thatf(0)<0 (semipositone). Assuming thatf′(∞)≡limt→∞f(t)> 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)′ When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how they evolve. This work extends and complements that of [3, 7] wheref′(∞)≦0.
Stable summands ofU(n)
Authors: Crabb M. C. , Hubbuck J. R. , McCall J. A. W. 
Published: November 2011

SynopsisThe special unitary groupSU(n)has the stable homotopy type of a wedge ofn− 1 finite complexes. The ‘first’ of these complexes is ΣℂPn–1, which is well known to be indecomposable at the prime 2 whethernis finite or infinite. We show that the ‘second’ finite complex is again indecomposable at the prime 2 whennis finite, but splits into a wedge of two pieces whennis infinite.
The viscous damping prevents propagation of singularities in the system of viscoelasticity
Authors: Rybka Piotr 
Published: November 2011

SynopsisWe show that the linear viscous damping Δut, is so strong that it altogether prevents propagation of singularities of the gradient of solutions to the system of viscoelasticity. Moreover, no creation or annihilation of singularities is possible in finite time.