We study the numerical solution of a singular free boundary problem for a second order nonlinear ordinary differential equation, where the differential operator is the degenerate m-Laplacian. A typical difficulty arising in free boundary problems is that the analytical solution may become non-smooth at one boundary or at both boundaries of the interval of integration. A numerical method propose...

ly u t is nothing more than an element in a Banach space B and this leaves room for applications to a wide variety of problems in di erential equations As in the examples above B might be L and A might be x or x and homogeneous boundary conditions could be included by restricting B appropriately More generally u t could be an vector valued function of multiple space variables The next step is t...

Comparative analysis of two ideologically distinct approaches in the theory of fuzzy di"erential equations is given. Domains of applications, advantages and shortcomings of those approaches are described. New de2nitions of solutions to fuzzy di"erential equations are proposed. c © 2002 Elsevier Science B.V. All rights reserved.

If u(t; x) is a solution of a one{dimensional, parabolic, second{order, linear partial di erential equation (PDE), then it is known that, under suitable conditions, the number of zero{crossings of the function u(t; ) decreases (that is, does not increase) as time t increases. Such theorems have applications to the study of blow{up of solutions of semilinear PDE, time dependent Sturm Liouville t...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

The suitability of methods from multidimensional systems theory and digital signal processing for the e cient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial di erential equation into a transfer function description of a multidimensional continuous system. It serves as the...

We consider the construction of geometric integrators in the class of RKMK methods. Any di erential equation in the form of an in nitesimal generator on a homogeneous space is shown to be locally equivalent to a di erential equation on the Lie algebra corresponding to the Lie group acting on the homogenous space. This way we obtain a distinction between the coordinate-free phrasing of the di er...

vol. 37 (2008) No. 1 Book review: LIMIT CYCLES OF DIFFERENTIAL EQUATIONS by Colin Christopher and Chengzhi Li In June 2006 Jaume Llibre and Armengol Gasull organized the Advan ed Course on Limit Cy les and Di erential Equations at the Centre de Re er a Matemàti a in Bar elona. There were three le turers: two by the authors of this book and by Sergey Yakovenko. The book under review ontains the ...

We present a block cipher that has the best performance of all 64-bit block ciphers with the smallest proven di erential/linear probability 2 62 using the structure proposed by Matsui. One of features of his methodology is to use some power functions in GF (2 n ) with di erent n that are resistant to di erential and linear attacks. In this paper we discuss how to combine power functions x k in ...