Travelling waves for a nonlocal double-obstacle problem

1997 ◽  
Vol 8 (6) ◽  
pp. 581-594 ◽  
Author(s):  
PAUL C. FIFE
Keyword(s):  
Obstacle Problem ◽  
Travelling Waves ◽  
Single Point ◽  
Travelling Wave ◽  
Wave Profile ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Piecewise Constant ◽  
Regularity Properties ◽  
Necessary And Sufficient

Existence, uniqueness and regularity properties are established for monotone travelling waves of a convolution double-obstacle problemut =J*u−u−f (u),the solution u(x, t) being restricted to taking values in the interval [−1, 1]. When u=±1, the equation becomes an inequality. Here the kernel J of the convolution is nonnegative with unit integral and f satisfies f(−1)>0>f(1). This is an extension of the theory in Bates et al. (1997), which deals with this same equation, without the constraint, when f is bistable. Among many other things, it is found that the travelling wave profile u(x−ct) is always ±1 for sufficiently large positive or negative values of its argument, and a necessary and sufficient condition is given for it to be piecewise constant, jumping from −1 to 1 at a single point.

Travelling wave solutions for an infection-age structured model with diffusion

2009 ◽  
Vol 139 (3) ◽  
pp. 459-482 ◽  
Author(s):  
A. Ducrot ◽  
P. Magal
Keyword(s):  
Travelling Waves ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Travelling Wave Solutions ◽  
Necessary And Sufficient Condition ◽  
Infection Age ◽  
Age Of Infection ◽  
Age Structured ◽  
Necessary And Sufficient ◽  
Age Structured Model

In this article, we study the existence of travelling waves for a class of epidemic models structured in space and with respect to the age of infection. We obtain a necessary and sufficient condition for the existence of travelling waves for such a class of problems. As a consequence of our main result, we also derive the existence of travelling waves of a class of functional partial derivative equations.

scholarly journals New Distributional Global Solutions for the Hunter-Saxton Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
C. O. R. Sarrico
Keyword(s):  
Travelling Waves ◽  
Solution Concept ◽  
Global Solutions ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Discontinuous Solutions ◽  
Consistent Extension ◽  
Distributional Product ◽  
Necessary And Sufficient

In the setting of a distributional product, we consider a Riemann problem for the Hunter-Saxton equation[ut+((1/2)u2)x]x=(1/2)ux2in a convenient space of discontinuous functions. With the help of a consistent extension of the classical solution concept, two classes of discontinuous solutions are obtained: one class of conservative solutions and another of dispersive solutions. A necessary and sufficient condition for the propagation of a distributional profile as a travelling wave is also presented, which allows identifying an interesting set of explicit distributional travelling waves. In the paper, we will show some results we have obtained by applying this framework to other equations and systems.

EQUIVALENT SEQUENTIAL AND PARALLEL REDUCTIONS IN ARBITRARY BINARY PICTURES

2014 ◽  
Vol 28 (07) ◽  
pp. 1460009 ◽  
Author(s):  
KÁLMÁN PALÁGYI
Keyword(s):  
Single Point ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Sufficient Criterion ◽  
Translation Invariant ◽  
Necessary And Sufficient

A reduction transforms a binary picture only by changing some black points to white ones, which is referred to as deletion. Sequential reductions traverse the black points of a picture, and consider a single point for possible deletion, while parallel reductions can delete a set of black points simultaneously. Two reductions are called equivalent if they produce the same result for each input picture. A deletion rule is said to be equivalent if it yields a pair of equivalent parallel and sequential reductions. This paper introduces a class of equivalent deletion rules that allows us to establish a new sufficient condition for topology-preserving parallel reductions in arbitrary binary pictures. In addition we present a method of verifying that a deletion rule given by matching templates is equivalent, a necessary and sufficient condition for order-independent deletion rules, and a sufficient criterion for order-independent and translation-invariant parallel subfield-based algorithms.

On the stability of some solutions of the Stefan problem

1991 ◽  
Vol 2 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Riccardo Ricci ◽  
Xie Weiqing
Keyword(s):  
Stefan Problem ◽  
Travelling Wave ◽  
Sufficient Condition ◽  
Travelling Wave Solutions ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Necessary And Sufficient ◽  
Travelling Wave Front

We investigate the stability of travelling wave solutions of the one-dimensional under-cooled Stefan problem. We find a necessary and sufficient condition on the initial datum under which the free boundary is asymptotic to a travelling wave front. The method applies also to other types of solutions.

scholarly journals On the ordinary convergence of restricted fourier series

1917 ◽  
Vol 93 (651) ◽  
pp. 276-292 ◽  
Keyword(s):  
Fourier Series ◽  
General Type ◽  
Closed Interval ◽  
Single Point ◽  
Interval Of Periodicity ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Trigonometrical Series ◽  
Derived Series ◽  
Necessary And Sufficient

1. The necessary and sufficient condition that a trigonometrical series should be a Fourier series is that the integrated series should converge to an integral throughout the closed interval of periodicity, and should be the Courier series, accordingly, of an integral. Conversely, starting with the Courier series of an integral and differentiating it term by term, we obtain the Courier series of the most general type, namely, one associated with any function possessing an absolutely convergent integral. If the Courier series which is differentiated is not the Courier series of an integral, but of a function which fails to be an integral, at even a single point, the derived series will not lie a Courier series.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

Sign in / Sign up

Export Citation Format

Share Document