bluuebunny/crossref_metadata_2025_split huggingface dataset:
Asymptotic behaviour of some reaction-diffusion systems modelling complex combustion on bounded domains
Authors: Avrin Joel D. 
Published: November 2011

SynopsisWe consider three models of multiple-step combustion processes on bounded spatial domains. Previously, steady-state convergence results have been established for these models with zero Neumann boundary conditions imposed on the temperature as well as the mass fractions. We retain here throughout the same boundary conditions on the mass fractions, but in our first set of results we establish steady-state convergence results with fixed Dirichlet boundary conditions on the temperature. Next, under certain physically reasonable assumptions, we develop, for two of the models, estimates on the decay rates of both mass fractions to zero, while for the remaining model we develop estimates on the decay rate of one concentration to zero and establish a positive lower bound on the other mass fraction. These results hold under either set of boundary conditions, but when the Dirichlet conditions are imposed on the temperature, we are able to obtain estimates on the rate of convergence of the temperature to its (generally nonconstant) steady-state. Finally, we improve the results of a previous paper by adding a temperature convergence result.
Estimates on the Green's function of second-order elliptic operators in ℝN
Authors: Hill Adrian T. 
Published: November 2011

Sharp upper and lower pointwise bounds are obtained for the Green's function of the equationfor λ> 0. Initially, in a Cartesian frame, it is assumed that . Pointwise estimates for the heat kernel of ut + Lu = 0, recently obtained under this assumption, are Laplace-transformed to yield corresponding elliptic results. In a second approach, the coordinate-free constraint is imposed. Within this class of operators, the equations defining the maximal and minimal Green's functions are found to be simple ODEs when written in polar coordinates, and these are soluble in terms of the singular Kummer confluent hypergeometric function. For both approaches, bounds on are derived as a consequence.
Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN
Authors: Xie Ziqing 
Published: November 2011

We consider the following problem:wherefor x ∈ RN, f(x, t), ft (x, t) ∈ C(RN × R), and f (x, t) ≧ 0 for all x ∈ RN and t ∈ R+, f(x, t) is an odd function of t. We show that if the maximum of Q(x) is achieved at k different points of RN, then for μ large enough the above problem has at least k positive solutions and k nodal solutions.
The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity
Authors: Shearer Michael , Yang Yadong 
Published: November 2011

Using the viscosity-capillarity admissibility criterion for shock waves, we solve the Riemann problem for the system of conservation lawswhere σ(u) = u3 − u. This system is hyperbolic at (u, v) unless . We find that the Riemann problem has a unique solution for all data in the hyperbolic regions, except for a range of data in the same phase (i.e. on the same side of the nonhyperbolic strip). In the nonunique cases, there are exactly two admissible solutions. The analysis is based upon a formula describing all saddle-to-saddle heteroclinic orbits for a family of cubic vector fields in the plane.
Realisation of ordinary differential equations by retarded functional differential equations in neighbourhoods of equilibrium points
Authors: Faria Teresa , Magalhães Luis T. 
Published: November 2011

This paper addresses the realisation of ordinary differential equations (ODEs) by retarded functional differential equations (FDEs) in finite-dimensional invariant manifolds, locally around equilibrium points. A necessary and sufficient condition for realisability of C1 vector fields is established in terms of their linearisations at the equilibrium.It is also shown that any arbitrary finite jet of vector fields of ODEs can be realised without any further restrictions than those imposed by the realisability of its linear term, a fact of relevance for discussing the flows defined by FDEs around singularities, and their bifurcations. Besides, it is proved that such a realisation can always be achieved with FDEs whose nonlinearities are defined in terms of a finite number of delayed values of the solutions.
Application of two parameter eigencurves to Sturm–Liouville problems with eigenparameter-dependent boundary conditions
Authors: Binding P. A. , Browne Patrick J. 
Published: November 2011

Oscillation, comparison and asymptotic theory for the Sturm-Liouville problemwith 1/p, q, r ε L1 ([0, 1]), p, r > 0, are studied subject to eigenvalue-dependent boundary conditionsThis continues previous work on cases with (− 1)j δj ≦ 0 where δj = ajdj − bjcj. We now consider the remaining sign conditions for δj, exploiting the interplay between the graph of cot θ− (λ, 1), for a modified Prüfer angle θ−, and the eigencurves of a related two-parameter problem.
Existence of two solutions of nonlinear elliptic equations with critical Sobolev exponents and mixed boundary conditions
Authors: Huang Feimin 
Published: November 2011

Let Ω be a bounded domain in Rn(n ≧ 3) with Lipschitz-continuous boundary, ∂Ω = Γ0∪Γ1. In this paper we consider the following problem:where φ ∈ L2 (Γ1), φ ≢ 0 on Γ1 and γ is the unit outward normal and p = 2n/(n − 2) = 2* is the critical exponent for the Sobolev embedding . We prove that for φ ∈ L2(Γ1) satisfying suitable conditions, the problem admits two solutions.
Stability and characteristic wavelength of planar interfaces in the large diffusion limit of the inhibitor
Authors: Taniguchi Masaharu , Nishiura Yasumasa 
Published: November 2011

A characteristic wavelength and its parametric dependency are studied for planar interfaces of activator-inhibitor systems as well as their stability in two-dimensional space. When an unstable planar interface is slightly perturbed in a random way, it develops with a characteristic wavelength, that is, the fastest-growing one. A natural question is to ask under what conditions this characteristic wavelength remains finite and approaches a positive definite value as the width of interface, say ε, tends to zero. In this paper, we show that the fastest-growing wavelength has a positive limit value as ε tends to zero for the system:This is a fundamental fact for stuyding the domain size of patterns in higher-space dimensions.
Least energy solutions for elliptic equations in unbounded domains
Authors: del Pino Manuel A. , Felmer Patricio L. 
Published: November 2011

In this paper we study the existence of least energy solutions to subcritical semilinear elliptic equations of the formwhere Ω is an unbounded domain inRNandfis aC1function, with appropriate superlinear growth. We state general conditions on the domain Ω so that the associated functional has a nontrivial critical point, thus yielding a solution to the equation. Asymptotic results for domains stretched in one direction are also provided.
Inequalities for a function involving its integral and derivative
Authors: Li Horng Jaan , Yeh Cheh Chih 
Published: November 2011

We give a concise approach to generalising the inequalities of Wirtinger, Hardy, Weyl and Opial by using the well-known inequality: if X and Y are non-negative, thenfor p > 1 (0 < p < 1), respectively.
Periodic solutions of planar systems with two delays
Authors: Ruan Shigui , Wei Junjie 
Published: November 2011

In this paper, we consider a planar system with two delays:ẋ1(t) = −a0x1(t) + a1F1 (x1(t − τ1), x2(τ−t2)).ẋ2(t) = −b0x2(t) + b1F2 (x1(t − τ1), x2(t − τxs2)).Firstly, linearized stability and local Hopf bifurcations are studied. Then, existence conditions for non-constant periodic solutions are derived using degree theory methods. Finally, a simple neural network model with two delays is analysed as an example.
Existence of bounded solutions of some nonlinear parabolic equations
Authors: Mokrane A. 
Published: November 2011

SynopsisThis paper proves the existence of (at least) one solution of the following equation:Here, is an elliptic operator of Leray-Lions type acting from into Lp′(0, T; W−1.p′ (Ω)), (1/p + 1/p′ = 1) and |F(u, ∇u)| ≧b(|u|)(l + |≧u|P). There are no smoothness assumptions on the bounded open set Ω; the operator and the nonlinearity F(u, ∇u) are denned in terms of Carathéodory functions. These points are the most characteristic features of this paper.Assuming the existence of upper and lower solutions allows us to obtain L∞(Q)-estimates. An estimate is then proved. The final step is to prove the strong convergence in of the approximations. This proof relies on the method introduced by L. Boccardo, F. Murat and J. P. Puel for elliptic and parabolic problems of this type.
Centraliser near-rings determined by fixed point free automorphism groups
Authors: Fuchs Peter , Maxson C. J. , Pettet M. R. , Smith K. C. 
Published: November 2011

SynopsisLet G be a group and let A be a fixed point free group of automorphisms of G. It is shown that the centraliser near-ring MA(G) has at most one nontrivial ideal. Conditions on the pair (A, G) are given which force MA(G) to be simple. It is shown that if a nonsimple near-ring MA(G) exists, then A and G have unusual properties.
Invariant manifolds in singular perturbation problems for ordinary differential equations
Authors: Sakamoto Kunimochi 
Published: November 2011

SynopsisBased on Fenichel's geometric idea, invariant manifold theory is applied to singular perturbation problems. This approach clarifies the nature of outer and inner solutions. A specific condition is given to ensure the existence of heteroclinic connections between normally hyperbolic invariant manifolds. A method to approximate the connections is also presented.
Periodic solutions of a planar delay equation
Authors: Táboas Plácido 
Published: November 2011

SynopsisWe study the planar delay differential equationx′(t)= −x(t)+αF(x(t − 1)), forα> 0. An existence theorem for nonconstant periodic solutions is achieved for a certain class of mapsF, forα> someα0. Besides a condition of nondegeneracy atx= 0, we assumeFis bounded and satisfies a kind ofplanar negative feedback condition. The nonconstant periodic solutions are associated with nontrivial fixed points of a certain operator defined by the flow in the plase space C([−l, 0], R2). In our approach, the existence of such fixed points depends on the ejectivity of O ϵC([−1, 0], R2) with respect to that operator. Relaxing the boundedness condition onF, we show the existence of a sequence of values ofα, α0<α1<…, where a Hopf bifurcation occurs.
A two-parameter eigenvalue problem involving complex potentials
Authors: Faierman M. 
Published: November 2011

SynopsisWe consider a two-parameter system of ordinary differential equations of the second order involving complex potentials and show that, unlike the case of real potentials, the eigenfunctions of the system do not necessarily form a complete set in the usual Hilbert space associated with the problem. We also give a necessary and sufficient condition for the eigenfunctions to be complete. Finally, we establish some results concerning the eigenvalues of the system.
Attractors of partial differential evolution equations in an unbounded domain
Authors: Babin A. V. , Vishik M. I. 
Published: November 2011

SynopsisThere is a large number of papers in which attractors of parabolic reaction-diffusion equations in bounded domains are investigated. In this paper, these equations are considered in the whole unbounded space, and a theory of attractors of such equations is built. While investigating these equations, specific difficulties arise connected with the noncompactness of operators, with the continuity of their spectra, etc. Therefore some new conditions on nonlinear terms arise. In this paper weighted spaces are widely applied. An important feature of this problem is worth mentioning: namely, properties of semigroups corresponding to equations with solutions in spaces of growing and of decreasing functions essentially differ.
Using Melnikov's method to solve Silnikov's problems
Authors: Lin Xiao-Biao 
Published: November 2011

SynopsisA function space approach is employed to obtain bifurcation functions for which the zeros correspond to the occurrence of periodic or aperiodic solutions near heteroclinic or homoclinic cycles. The bifurcation function for the existence of homoclinic solutions is the limiting case where the period is infinite. Examples include generalisations of Silnikov's main theorems and a retreatment of a singularly perturbed delay differential equation.
A functional-analytic framework for the study of elliptic equations on variable domains
Authors: Vegas José M. 
Published: November 2011

SynopsisGiven a decreasing sequence of domains Ωnconverging in measure to some domain Ω0, a sequence of subspacesVof a Hilbert spaceVis constructed in such a way that the convergence of the solutions ofu−Δu=fon Ωnwith Neumann Boundary Condition is given in terms of the convergence of the orthogonal projectionsPnonVn. Under dissipative assumptions, we can obtain continuation results for equations likeu−Δu=f(x,u∇u).
Balanced big Cohen-Macaulay modules and free extensions of local rings
Authors: Riley Adrian M. 
Published: November 2011

SynopsisLet A and B be commutative Noetherian local rings, such that B is a finitely generated free A-module. It is shown that if M is a balanced big Cohen–Macaulay A-module (that is, every system of parameters for A is an M-sequence), then M⊗AB is a balanced big Cohen-Macaulay B-module.
Über die C2-Kompaktheit der Bahn von Lösungen semflinearer parabolischer Systeme
Authors: Redlinger Reinhard 
Published: November 2011

SynopsisThe semilinear parabolic systemut+A(x, D)u=g(u) in (0, ∞) × Ω, Ω⊂ℝnbounded,u∈ ℝN, with homogeneous boundary conditionsB(x, D)u=0 on (0, ∞)×∂Ω is considered. The non-linearitygis assumed to be locally Lipschitz-continuous. It is shown that the orbit of a bounded regular solutionuis relatively compact in.
Multiparameter problems and joint spectra
Authors: McGhee D. F. 
Published: November 2011

SynopsisIn this paper, we demonstrate an intimate connection between the spectrum of a multiparameter problem and the joint spectrum of an associated set of commuting operators, and show that the spectrum of a multiparameter problem involving bounded operators is non-empty. Multiparameter systems involving compact and self-adjoint operators are considered, and some simplification of results in the literature are noted.
Pointwise convergence of eigenfunction expansions, associated with a pair of ordinary differential expressions
Authors: Coddington Earl A. , Dijksma Aalt , de Snoo Hendrik S. V. 
Published: November 2011

SynopsisFor the differential equation Lf = λMf on an open interval of ℝ, a theory in terms of relations in a Hilbert space associated with M was developed in a paper by Coddington and de Snoo, and eigenfunction expansions were derived in a paper by Dijksma and de Snoo. In the case of a regular problem on a compact interval, pointwise convergence of the expansions was shown in another paper by Coddington and de Snoo. Here, we show pointwise convergence in the general singular case.
Regularly solvable extensions of non-self-adjoint ordinary differential operators
Authors: Evans W. D. 
Published: November 2011

SynopsisLetL0,M0be closed densely defined linear operators in a Hilbert spaceHwhich form an adjoint pair, i.e.. In this paper, we study closed operatorsSwhich satisfyand are regularly solvable in the sense of Višik. The abstract results obtained are applied to operators generated by second-order linear differential expressions in a weighted spaceL2(a, b; w).
The asymptotic form of the Titchmarsh–Weyl coefficient for a fourth order differential equation
Authors: Hinton D. B. , Shaw J. K. 
Published: November 2011

SynopsisThis paper considers the asymptotic form, as λ tends to infinity in sectors omitting the real axis, of the matrix Titchmarsh-Weyl coefficient M(λ) for the fourth order equation y(4) + q(x)y = λy, where q(x) is real and locally absolutely integrable. By letting M0(λ) denote the m-coefficient for the Fourier case y(4) = λy, the asymptotic formula M(λ) = M0(λ) + 0(1) is established.
A note on the domain characterization of certain Schrödinger operators with strongly singular potentials
Authors: Kalf Hubert 
Published: November 2011

SynopsisFor β > β0: = 1 −[(n − 2)/2]2 and n ≧ 2, it was recently shown by Simon that the self-adjoint operator associated with −Δ + βr−2 in L2(ℝn) has domain H2(ℝn) ∩D(r−2) the constant β0 being the best possible. An alternative proof of this result is given.
Integral mean value theorems and the Ganelius inequality
Authors: Knowles Ian 
Published: November 2011

SynopsisThe inequality of Ganelius states that, for suitable functions f and g on an interval [a, b], [inf f + var f]sup ∫ jdg, where the supremum is taken over all sub-intervals J of [a, b]. A more general version of this inequality is derived as well as certain related generalized mean-value theorems.
On regularization of right hand sides of differential relations
Authors: Kurzweil Jaroslav , Jarník Jiří 
Published: November 2011

SynopsisLet the values ofFbe convex compact subsets ofRnand letFbe upper semicontinuous with respect tox. There are two ways known of replacingFby a more regular map so that the set of solutions of (2) remains unchanged. We prove that both ways lead to the same more regular map and extend the results to the case whereRnis replaced by a separable Banach space.
A Friedrichs inequality and an application
Authors: Lewis Roger T. 
Published: November 2011

SynopsisAn inequality whose origins date to the work of G. H. Hardy is presented. This Hardy-type inequality applies to derivatives of arbitrary order of functions whose domain is a subset of ℝn. The Friedrichs inequality is a corollary. The result is then used to establish lower bounds on the essential spectra of even-order elliptic partial differential operators on unbounded domains.
An extension of the Sturm–Picone theorem to elliptic differential equations
Authors: Müller-Pfeiffer E. 
Published: November 2011

SynopsisThe paper presents an extension of the well-known Sturm–Picone theorem for self-adjoint equations to the n-dimensional case. The basic domain G ⊆ Rn is possibly unbounded and no regularity hypotheses on the boundary ∂G are required. The coefficients of the elliptic equation may also be unbounded on G.
T-periodic solutions for some second order differential equations with singularities
Authors: del Pino Manuel , Manásevich Raúl , Montero Alberto 
Published: November 2011

SynopsisWe study the existence of T-periodic positive solutions of the equationwhere f(t, .) has a singularity of repulsive type near the origin. Under the assumption that f(t, x) lies between two lines of positive slope for large and positive x, we find a non-resonance condition which predicts the existence of one T-periodic solution.Our main result gives a Fredholm alternative-like result for the existence of T-periodic positive solutions for
Characterisation of the factors of quasi-differential expressions
Authors: Race D. , Zettl A. 
Published: November 2011

SynopsisA necessary and sufficient condition for a general, scalar, quasi-differential expression of order n to be factorisable into a product of expressions of order n − k and k, for any 0 < k < n, is given. The factors are characterised completely in terms of elements of the null space of the expression and its adjoint. The results obtained extend existing results due to both Polya and Zettl from the case of classical linear differential expressions to quasi-differential expressions.
Chapter 4 of Ramanujan's Second Notebook
Authors: Berndt Bruce C. , Wilson B. M. 
Published: November 2011

SynopsisThe purpose of this paper is to examine the content of Chapter 4 of Ramanujan's second notebook. The first half of this chapter is on iterates of the exponential function. The second half focuses upon an interesting formal procedure which Ramanujan, in particular, used in the theory of integral transforms.
Monotone methods and attractivity results for Volterra integro-partial differential equations
Authors: Schiaffino Andrea , Tesei Alberto 
Published: November 2011

SynopsisA Volterra integro-partial differential equation of parabolic type, which describes the time evolution of a population in a bounded habitat, subject both to past history and space diffusion effects, is investigated; general homogeneous boundary conditions are admissible. Under suitable conditions, the unique nontrivial nonnegative equilibrium is shown to be globally attractive in the supremum norm. Monotone methods are the main tool of the proof.
On the exponential behaviour of eigenfunctions and the essential spectrum of differential operators
Authors: Atkinson F. V. , Evans W. D. 
Published: November 2011

SynopsisThe paper deals with the differential equationon [ 0, ∞) Where λ>0 and the coefficients qm are complex-valued with qn continuous and non-zero, w is positive and continuous and qm for m = 0, 1,…, n − 1. In the first part of the paper the exponential behaviour of any solution of (*) is given in terms of a function ρ(λ) which is roughly the distance of λ from the essential spectrum of a closed, densely denned linear operator T generated by T+ in L2(0, ∞ w). Next, estimates are obtained for the solutions in terms of the coefficients in (*). When the latter results are compared with the estimates established previously in terms of ρ(λ), bounds for ρ(λ) are obtained. From the general result there are two kinds of consequences. In the first, criteria for ρ(λ) = 0 for all All λ > 0 are obtained; this means that [0, ∞) lies in the essential spectrum of T in appropriate circumstances. The second type of consequence concerns bounds of the form ρ(λ) = O(λr) for λ → ∞ and r<1.
Immigrant–native differences in employment-based retirement plan participation
Authors: HEIM BRADLEY T. , LURIE ITHAI Z. , RAMNATH SHANTHI P. 
Published: November 2011

AbstractThis paper examines differences between immigrant and native employees in retirement plan participation using SIPP data. We find that the participation rate among natives is 60 percent, while the native-immigrant participation gap ranges from 10.9 percentage points for naturalized citizens to 35.4 percentage points for non-permanent residents. Controlling for demographic and job characteristics can explain up to half of the gap. Decomposing the overall immigrant-native difference into differences in employer offers, plan eligibility, and plan take-up shows that the likelihood of working for an employer that offers a plan is the primary driver of the overall gap.
Probabilistic tsunami hazard in the Mediterranean Sea
Authors: Sørensen Mathilde B. , Spada Matteo , Babeyko Andrey , Wiemer Stefan , Grünthal Gottfried 
Published: November 2011

Estimating the occurrence probability of natural disasters is critical for setting construction standards and, more generally, prioritizing risk mitigation efforts. Tsunami hazard in the Mediterranean region has traditionally been estimated by considering so‐called “most credible” scenarios of tsunami impact for limited geographical regions, but little attention has been paid to the probability of any given scenario. We present here the first probabilistic estimate of earthquake‐generated tsunami hazard for the entire Mediterranean Sea. We estimate the annual probability of exceeding a given tsunami amplitude at any coastal location in the region by applying a Monte Carlo based technique. Earthquake activity rates are estimated from the observed seismicity, and tsunami impact is derived from deterministic tsunami wave propagation scenarios. The highest hazard is in the eastern Mediterranean owing to earthquakes along the Hellenic Arc, but most of the Mediterranean coastline is prone to tsunami impact. Our method allows us to identify the main sources of tsunami hazard at any given location and to investigate the potential for issuing timely tsunami warnings. We find that the probability of a tsunami wave exceeding 1 m somewhere in the Mediterranean in the next 30 years is close to 100%. This underlines the urgent need for a tsunami warning system in the region.