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Evolution Problem (evolution + problem)

Distribution by Scientific Domains
Mathematics and Statistics60%
Engineering40%

Selected Abstracts

Models of non-smooth switches in electrical systems

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2005
Christoph Glocker
Abstract Idealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of set-valued functions, which allow to formulate the circuit's dynamic behaviour as a differential inclusion. This approach is demonstrated by the example of the DC,DC buck converter. A difference scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the set-valued branch relations in order to obtain a minimal model, is performed on the example of the buck converter. Copyright © 2005 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]

Asymptotic behaviour for a two-dimensional thermoelastic model

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2007
M. Fabrizio
Abstract In this paper we study a thermoelastic material with an internal structure which binds the materials fibres to a quadratic behaviour. Moreover, a hereditary constitutive law for heat flux is supposed. We prove results of asymptotic stability and exponential decay for the evolution problem in two-dimensional space domain. Copyright © 2006 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]

Uniform stabilization of a one-dimensional hybrid thermo-elastic structure

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2003
Marié Grobbelaar-Van Dalsen
Abstract This paper is concerned with the stabilization of a one-dimensional hybrid thermo-elastic structure consisting of an extensible thermo-elastic beam which is hinged at one end with a rigid body attached to its free end. The model takes account of the effect of stretching on bending and rotational inertia. The property of uniform stability of the energy associated with the model is asserted by constructing an appropriate Lyapunov functional for an abstract second order evolution problem. Critical use is made of a multiplier of an operator theoretic nature, which involves the fractional power A,1/2 of the bi-harmonic operator pair A acting in the abstract evolution problem. An explicit decay rate of the energy is obtained. Copyright © 2003 John Wiley & Sons, Ltd. [source]

The minimum evolution problem: Overview and classification

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2009
Daniele Catanzaro
Abstract Molecular phylogenetics studies the hierarchical evolutionary relationships among organisms by means of molecular data. These relationships are typically described by means of weighted trees, or phylogenies, whose leaves represent the observed organisms, internal vertices the intermediate ancestors, and edges the evolutionary relationships between pairs of organisms. Molecular phylogenetics provides several criteria for selecting one phylogeny from among plausible alternatives. Usually, such criteria can be expressed in terms of objective functions, and the phylogenies that optimize them are referred to as optimal. One of the most important criteria is the minimum evolution (ME) criterion, which states that the optimal phylogeny for a given set of organisms is the one whose sum of edge weights is minimal. Finding the phylogeny that satisfies the ME criterion involves solving an optimization problem, called the minimum evolution problem (MEP), which is notoriously -Hard. This article offers an overview of the MEP and discusses the different versions of it that occur in the literature. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009 [source]

Discontinuous Galerkin framework for adaptive solution of parabolic problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2007
Deepak V. Kulkarni
Abstract Non-conforming meshes are frequently employed in adaptive analyses and simulations of multi-component systems. We develop a discontinuous Galerkin formulation for the discretization of parabolic problems that weakly enforces continuity across non-conforming mesh interfaces. A benefit of the DG scheme is that it does not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. The salient features of the formulation are highlighted through an a priori analysis. When coupled with a mesh refinement scheme the DG formulation is able to accommodate multiple hanging nodes per element edge and leads to an effective adaptive framework for the analysis of interface evolution problems. We demonstrate our approach by analysing the Stefan problem of solidification. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A class of parallel multiple-front algorithms on subdomains

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003
A. Bose
Abstract A class of parallel multiple-front solution algorithms is developed for solving linear systems arising from discretization of boundary value problems and evolution problems. The basic substructuring approach and frontal algorithm on each subdomain are first modified to ensure stable factorization in situations where ill-conditioning may occur due to differing material properties or the use of high degree finite elements (p methods). Next, the method is implemented on distributed-memory multiprocessor systems with the final reduced (small) Schur complement problem solved on a single processor. A novel algorithm that implements a recursive partitioning approach on the subdomain interfaces is then developed. Both algorithms are implemented and compared in a least-squares finite-element scheme for viscous incompressible flow computation using h - and p -finite element schemes. Copyright © 2003 John Wiley & Sons, Ltd. [source]

On non-Newtonian incompressible fluids with phase transitions

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2006
Namkwon Kim
Abstract A modified model for a binary fluid is analysed mathematically. The governing equations of the motion consists of a Cahn,Hilliard equation coupled with a system describing a class of non-Newtonian incompressible fluid with p -structure. The existence of weak solutions for the evolution problems is shown for the space dimension d=2 with p, 2 and for d=3 with p, 11/5. The existence of measure-valued solutions is obtained for d=3 in the case 2, p< 11/5. Similar existence results are obtained for the case of nondifferentiable free energy, corresponding to the density constraint |,| , 1. We also give regularity and uniqueness results for the solutions and characterize stable stationary solutions. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Numerical solution of a minimax ergodic optimal control problem

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Aragone Laura S.
In this work we consider an L, minimax ergodic optimal control problem with cumulative cost. We approximate the cost function as a limit of evolutions problems. We present the associated Hamilton-Jacobi-Bellman equation and we prove that it has a unique solution in the viscosity sense. As this HJB equation is consistent with a numerical procedure, we use this discretization to obtain a procedure for the primitive problem. For the numerical solution of the ergodic version we need a perturbation of the instantaneous cost function. We give an appropriate selection of the discretization and penalization parameters to obtain discrete solutions that converge to the optimal cost. We present numerical results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]