Global Solutions (global + solution)

Distribution by Scientific Domains


Selected Abstracts


Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2006
Slim Ibrahim
We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a semilinear Klein-Gordon equation in two space dimensions. Our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method. © 2006 Wiley Periodicals, Inc. [source]


Geometric transitions on non-Kähler manifolds

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 1 2007
A. Knauf
This article is based on the publications [1,3] and the author's PhD-thesis. We study geometric transitions on the supergravity level using the basic idea of [1], where a pair of non-Kähler backgrounds was constructed, which are related by a geometric transition. Here we embed this idea into an orientifold setup as suggested in [3]. The non-Kähler backgrounds we obtain in type IIA are non-trivially fibered due to their construction from IIB via T-duality with Neveu,Schwarz flux. We demonstrate that these non-Kähler manifolds are not half-flat and show that a symplectic structure exists on them at least locally. We also review the construction of new non-Kähler backgrounds in type I and heterotic theory as proposed in [2]. They are found by a series of T- and S-duality and can be argued to be related by geometric transitions as well. A local toy model is provided that fulfills the flux equations of motion in IIB and the torsional relation in heterotic theory, and that is consistent with the U-duality relating both theories. For the heterotic theory we also propose a global solution that fulfills the torsional relation because it is similar to the Maldacena,Nunez background. [source]


Support vector machines-based generalized predictive control

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 17 2006
S. Iplikci
Abstract In this study, we propose a novel control methodology that introduces the use of support vector machines (SVMs) in the generalized predictive control (GPC) scheme. The SVM regression algorithms have extensively been used for modelling nonlinear systems due to their assurance of global solution, which is achieved by transforming the regression problem into a convex optimization problem in dual space, and also their higher generalization potential. These key features of the SVM structures lead us to the idea of employing a SVM model of an unknown plant within the GPC context. In particular, the SVM model can be employed to obtain gradient information and also it can predict future trajectory of the plant output, which are needed in the cost function minimization block. Simulations have confirmed that proposed SVM-based GPC scheme can provide a noticeably high control performance, in other words, an unknown nonlinear plant controlled by SVM-based GPC can accurately track the reference inputs with different shapes. Moreover, the proposed SVM-based GPC scheme maintains its control performance under noisy conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Global optimization for robust control synthesis based on the Matrix Product Eigenvalue Problem

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2001
Yuji Yamada
Abstract In this paper, we propose a new formulation for a class of optimization problems which occur in general robust control synthesis, called the Matrix Product Eigenvalue Problem (MPEP): Minimize the maximum eigenvalue of the product of two block-diagonal positive-definite symmetric matrices under convex constraints. This optimization class falls between methods of guaranteed low complexity such as the linear matrix inequality (LMI) optimization and methods known to be NP-hard such as the bilinear matrix inequality (BMI) formulation, while still addressing most robust control synthesis problems involving BMIs encountered in applications. The objective of this paper is to provide an algorithm to find a global solution within any specified tolerance , for the MPEP. We show that a finite number of LMI problems suffice to find the global solution and analyse its computational complexity in terms of the iteration number. We prove that the worst-case iteration number grows no faster than a polynomial of the inverse of the tolerance given a fixed size of the block-diagonal matrices in the eigenvalue condition. Copyright 2001 © John Wiley & Sons, Ltd. [source]


Global existence and blow-up of the solutions for the multidimensional generalized Boussinesq equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2007
Ying Wang
Abstract In this paper, the existence and the uniqueness of the global solution for the Cauchy problem of the multidimensional generalized Boussinesq equation are obtained. Furthermore, the blow-up of the solution for the Cauchy problem of the generalized Boussinesq equation is proved. Copyright © 2007 John Wiley & Sons, Ltd. [source]


Semilinear wave equation with time dependent potential

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2004
Nicola Visciglia
Abstract We consider the following semilinear wave equation: (1) for (t,x) , ,t × ,. We prove that if the potential V(t,x) is a measurable function that satisfies the following decay assumption: ,V(t,x),,C(1+t)(1+,x,) for a.e. (t,x) , ,t × , where C, ,0>0 are real constants, then for any real number , that satisfies there exists a real number ,(f,g,,)>0 such that the equation has a global solution provided that 0<,,,(f,g,,). Copyright © 2004 John Wiley & Sons, Ltd. [source]


Mathematical analysis and stability of a chemotaxis model with logistic term

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2004
J. Ignacio Tello
Abstract In this paper we study a non-linear system of differential equations arising in chemotaxis. The system consists of a PDE that describes the evolution of a population and an ODE which models the concentration of a chemical substance. We study the number of steady states under suitable assumptions, the existence of one global solution to the evolution problem in terms of weak solutions and the stability of the steady states. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Contrasting Entrepreneurial Economic Development in Emerging Latin American Economies: Applications and Extensions of Resource-Based Theory

ENTREPRENEURSHIP THEORY AND PRACTICE, Issue 1 2008
G. Page West III
Emerging economies face daunting economic development challenges. Economists and management consultants have generally suggested global solutions that typically focus solely on foreign direct investment. Yet a resource-based theory approach offers an alternative view of economic development in which a foundation of resources within a region gestates entrepreneurial activity. While theoretically appealing, it is unclear in application how such resources can be developed or which types of resources are most important to develop. This paper extends the application of resource-based theory to entrepreneurial economic development in subsistence economies. A qualitative study of contrasting entrepreneurial activity in Chiapas (Mexico) and Atenas (Costa Rica) highlights the primacy of intangible resources,and especially entrepreneurial orientation resources,in the gestation of entrepreneurial activity. [source]


Keeping it real: anticounterfeiting strategies in the pharmaceutical industry

MANAGERIAL AND DECISION ECONOMICS, Issue 5 2008
Kristina M. LybeckerArticle first published online: 19 MAR 200
Although pharmaceutical counterfeiting incidents can be traced back thousands of years, it has been downplayed and even dismissed by pharmaceutical manufacturers in the past. That has changed. Pharmaceutical firms are newly dedicated to eradicate counterfeits globally and spending more money on anticounterfeiting efforts than ever before. The confluence of three factors seems to have drastically changed the existing paradigm for the pharmaceutical industry: increasing globalization, advancing technology, and the controversies surrounding the WTO Trade-related Aspects of Intellectual Property Rights Agreement and access to medicines. Given that counterfeit pharmaceuticals slip into the supply chain at every link, multinational pharmaceutical firms are searching for global solutions through increased interfirm cooperation along the supply chain. This research presents a theoretical model for characterizing the implications of these interventions on the motivations driving counterfeiters. The interventions are shown to increase the share of real pharmaceuticals and decrease the welfare losses attributable to counterfeiting. In practice, it is too early to evaluate the success of these new measures, but this research reflects on the extent of cooperation both across the supply chain and national boundaries and examines the likely long-run implications of these measures. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Global well-posedness of the Cauchy problem for certain magnetohydrodynamic-, models

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2010
Yi Du
Abstract This paper is devoted to study the Cauchy problem for certain incompressible magnetohydrodynamics-, model. In the Sobolev space with fractional index s>1, we proved the local solutions for any initial data, and global solutions for small initial data. Furthermore, we also prove that as ,,0, the MHD-, model reduces to the MHD equations, and the solutions of the MHD-, model converge to a pair of solutions for the MHD equations. Copyright © 2010 John Wiley & Sons, Ltd. [source]


The steady states and convergence to equilibria for a 1-D chemotaxis model with volume-filling effect

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2010
Yanyan Zhang
Abstract We consider a chemotaxis model with volume-filling effect introduced by Hillen and Painter. They also proved the existence of global solutions for a compact Riemannian manifold without boundary. Moreover, the existence of a global attractor in W1, p(,,,n), p>n, p,2, was proved by Wrzosek. He also proved that the ,-limit set consists of regular stationary solutions. In this paper, we prove that the 1-D stationary problem has at most an infinitely countable number of regular solutions. Furthermore, we show that as t,, the solution of the 1-D evolution problem converges to an equilibrium in W1, p, p,2. Copyright © 2009 John Wiley & Sons, Ltd. [source]


On the global existence and small dispersion limit for a class of complex Ginzburg,Landau equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2009
Hongjun Gao
Abstract In this paper we consider a class of complex Ginzburg,Landau equations. We obtain sufficient conditions for the existence and uniqueness of global solutions for the initial-value problem in d -dimensional torus ,,d, and that solutions are initially approximated by solutions of the corresponding small dispersion limit equation for a period of time that goes to infinity as dispersive coefficient goes to zero. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Existence of global solutions to a model of chondrogenesis

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2009
B. Kazmierczak
Abstract The paper considers conditions sufficient for the existence of classical C solutions to a new model of chondrogenesis during the vertebrate limb formation. We assume that the diffusion coefficient of the fibronectin is positive and that the function describing the interaction between the fibronectin and cells satisfies some additional properties. Copyright © 2008 John Wiley & Sons, Ltd. [source]


Existence and non-existence of global solutions of a non-local wave equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2004
Azmy S. Ackleh
Abstract We study the initial value problem where with ,(x),0 and . We show that solutions exist globally for 01. We also present the growth rate at blow-up. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Evolution completeness of separable solutions of non-linear diffusion equations in bounded domains

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2004
V. A. Galaktionov
Abstract As a basic example, we consider the porous medium equation (m > 1) (1) where , , ,N is a bounded domain with the smooth boundary ,,, and initial data . It is well-known from the 1970s that the PME admits separable solutions , where each ,k , 0 satisfies a non-linear elliptic equation . Existence of at least a countable subset , = {,k} of such non-linear eigenfunctions follows from the Lusternik,Schnirel'man variational theory from the 1930s. The first similarity pattern t,1/(m,1),0(x), where ,0 > 0 in ,, is known to be asymptotically stable as t , , and attracts all nontrivial solutions with u0 , 0 (Aronson and Peletier, 1981). We show that if , is discrete, then it is evolutionary complete, i.e. describes the asymptotics of arbitrary global solutions of the PME. For m = 1 (the heat equation), the evolution completeness follows from the completeness-closure of the orthonormal subset , = {,k} of eigenfunctions of the Laplacian , in L2. The analysis applies to the perturbed PME and to the p -Laplacian equations of second and higher order. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Initial boundary value problem for a class of non-linear strongly damped wave equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2003
Yang Zhijian
The paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non-linear wave equations. By a H00.5ptk-Galerkin approximation scheme, it proves that the above-mentioned problem admits a unique classical solution depending continuously on initial data and decaying to zero as t,+,as long as the non-linear terms are sufficiently smooth; they, as well as their derivatives or partial derivatives, are of polynomial growth order and the initial energy is properly small. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Global existence of weak-type solutions for models of monotone type in the theory of inelastic deformations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2002
Krzysztof Che
This article introduces the notion of weak-type solutions for systems of equations from the theory of inelastic deformations, assuming that the considered model is of monotone type (for the definition see [Lecture Notes in Mathematics, 1998, vol. 1682]). For the boundary data associated with the initial-boundary value problem and satisfying the safe-load condition the existence of global in time weak-type solutions is proved assuming that the monotone model is rate-independent or of gradient type. Moreover, for models possessing an additional regularity property (see Section 5) the existence of global solutions in the sense of measures, defined by Temam in Archives for Rational Mechanics and Analysis, 95: 137, is obtained, too. Copyright © 2002 John Wiley & Sons, Ltd. [source]


Global well-posedness for compressible Navier-Stokes equations with highly oscillating initial velocity

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2010
Qionglei Chen
In this paper, we prove global well-posedness for compressible Navier-Stokes equations in the critical functional framework with the initial data close to a stable equilibrium. This result allows us to construct global solutions for the highly oscillating initial velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms. © 2010 Wiley Periodicals, Inc. [source]


On the initial-boundary value problem of the incompressible viscoelastic fluid system

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 4 2008
Fanghua Lin
In this paper, we shall establish the local well-posedness of the initial-boundary value problem of the viscoelastic fluid system of the Oldroyd model. We shall also prove that the local solutions can be extended globally and that the global solutions decay exponentially fast as time goes to infinity provided that the initial data are sufficiently close to the equilibrium state. © 2007 Wiley Periodicals, Inc. [source]


Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 11 2006
Slim Ibrahim
We prove the existence and uniqueness of global solutions for a Cauchy problem associated to a semilinear Klein-Gordon equation in two space dimensions. Our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method. © 2006 Wiley Periodicals, Inc. [source]