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Suitable Assumptions (suitable + assumption)

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Mathematics and Statistics80%

Selected Abstracts

On a Penrose,Fife type system with Dirichlet boundary conditions for temperature

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2003
Gianni Gilardi
We deal with the Dirichlet problem for a class of Penrose,Fife phase field models for phase transitions. An existence result is obtained by approximating the non-homogeneous Dirichlet condition with classical third type conditions on the heat flux at the boundary of the domain where the model is considered. Moreover, we prove a regularity and uniqueness result under stronger assumptions on the regularity of the data. Suitable assumptions on the behaviour of the heat flux at zero and +,are considered. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solvers

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2001
Janne Martikainen
Abstract The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial differential eigenvalue problems in two- or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the inverted eigenvalue problem. Under suitable assumptions, the number of Lanczos iterations is shown to be independent of the problem size. The arising linear problems are solved using some standard fast elliptic solver. Numerical experiments demonstrate that the inverted problem is much easier to solve with the Lanczos algorithm that the original problem. In these experiments, the underlying Poisson and elasticity problems are solved using a standard multigrid method. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Convergence rates toward the travelling waves for a model system of the radiating gas

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007
Masataka Nishikawa
Abstract The present paper is concerned with an asymptotics of a solution to the model system of radiating gas. The previous researches have shown that the solution converges to a travelling wave with a rate (1 + t),1/4 as time t tends to infinity provided that an initial data is given by a small perturbation from the travelling wave in the suitable Sobolev space and the perturbation is integrable. In this paper, we make more elaborate analysis under suitable assumptions on initial data in order to obtain shaper convergence rates than previous researches. The first result is that if the initial data decays at the spatial asymptotic point with a certain algebraic rate, then this rate reflects the time asymptotic convergence rate. Precisely, this convergence rate is completely same as the spatial convergence rate of the initial perturbation. The second result is that if the initial data is given by the Riemann data, an admissible weak solution, which has a discontinuity, converges to the travelling wave exponentially fast. Both of two results are proved by obtaining decay estimates in time through energy methods with suitably chosen weight functions. 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]

A simple solution to the k -core problem

RANDOM STRUCTURES AND ALGORITHMS, Issue 1-2 2007
Svante Janson
Abstract We study the k -core of a random (multi)graph on n vertices with a given degree sequence. We let n ,,. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the degree sequence that imply that with high probability the k -core is empty and other conditions that imply that with high probability the k -core is non-empty and the sizes of its vertex and edge sets satisfy a law of large numbers; under suitable assumptions these are the only two possibilities. In particular, we recover the result by Pittel, Spencer, and Wormald (J Combinator Theory 67 (1996), 111,151) on the existence and size of a k -core in G(n,p) and G(n,m), see also Molloy (Random Struct Algor 27 (2005), 124,135) and Cooper (Random Struct Algor 25 (2004), 353,375). Our method is based on the properties of empirical distributions of independent random variables and leads to simple proofs. © 2006 Wiley Periodicals, Inc. Random Struct. Alg.,, 2007 [source]