Results 321 to 330 of about 3,258,064 (367)

Cauchy Singular Equations

2002
We first define singular integral equations of both the first and second kinds (SKI and SK2) with the Cauchy kernel (also called Cauchy singular equations) and then present some useful numerical methods to solve them. These equations are encountered in many applications in aerodynamics, elasticity, and other areas.
Pratap Puri, Prem K. Kythe
openaire   +2 more sources

Paralinearization of the Muskat Equation and Application to the Cauchy Problem

Archive for Rational Mechanics and Analysis, 2019
We paralinearize the Muskat equation to extract an explicit parabolic evolution equation having a compact form. This result is applied to give a simple proof of the local well-posedness of the Cauchy problem for rough initial data, in homogeneous Sobolev
T. Alazard, O. Lazar
semanticscholar   +1 more source

On The Generalized Cauchy Equation

Canadian Journal of Mathematics, 1967
It is the purpose of this note to prove the following theorem: Let ƒ: G → R be a non-constant continuous function with G a locally compact connected topological group and with R the real numbers. Let C = ƒ(G) and suppose that F: C × C → C is a junction such thatThen ƒ is monotone and open and F is continuous.
openaire   +2 more sources

Local Pexider and Cauchy equations

Aequationes mathematicae, 2007
Without assuming regularity we answer the questions when from a connected open set \(D \subset {\mathbb{R}}^2\) there exist quasiextensions of the Cauchy equation $$e(s + t) = e(s)e(t)\quad ((s, t) \in D)$$ and extensions of the Pexider equation $$f(s + t) = g(s)h(t)\quad ((s, t) \in D)$$ to \({\mathbb{R}}^2\).
J. Aczel, SKOF, Fulvia
openaire   +3 more sources

Cauchy's equation on Δ+

Aequationes Mathematicae, 1991
Recently R. C. Powers characterized the order automorphisms of the space of nondecreasing functions from one compact real interval to another [6, 7]. In this paper we show how his results, as well as the lattice-theoretic techniques which he employed, can be used to obtain solutions of Cauchy's equation for certain classes of semigroups (triangle ...
openaire   +2 more sources

Basic Equations: Cauchy and Pexider Equations [PDF]

, 2009
In this chapter, Cauchy’s fundamental equations are studied, some algebraic conditions and generalizations are considered, and alternate equations, conditions on restricted domains, Jensen’s equation, some special cases of Cauchy’s equations, extensions of the additive equations, Pexider equations and their extensions, some applications in economics ...
openaire   +1 more source

Cauchy’s functional equation and extensions: Goldie’s equation and inequality, the Gołąb–Schinzel equation and Beurling’s equation

, 2014
The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its ...
N. Bingham, A. Ostaszewski
semanticscholar   +1 more source

A Cauchy inequality for the Boltzmann equation

Mathematical Methods in the Applied Sciences, 2000
The distance to a set of Maxwellians is determined for a family of functions with bounded mass, energy and a small entropy production term. Functions with small masses are close to the null Maxwellian. Functions with masses bounded from below by a constant are approached by functions proportional to the gain term of the Boltzmann operator, taking ...
openaire   +2 more sources

The hyperstability of general linear equation via that of Cauchy equation

Aequationes Mathematicae, 2018
T. Phochai, S. Saejung
semanticscholar   +1 more source

On the alienation of the exponential Cauchy equation and the Hosszú equation

, 2016
Gyula Maksa, M. Sablik
semanticscholar   +1 more source