Displaying 21 – 40 of 335

Showing per page

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise, Sarah Cochez-Dhondt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space V that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into V. We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete problems...

An Algebraic Approach to Implicit Evolution Equations

Wha-Suck Lee, Niko Sauer (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

A Banach algebra homomorphism on the convolution algebra of integrable functions is the essence of Kisyński's equivalent formulation of the Hille-Yosida theorem for analytic semigroups. For the study of implicit evolution equations the notion of empathy happens to be more appropriate than that of semigroup. This approach is based upon the intertwining of two families of evolution operators and two families of pseudo-resolvents. In this paper we show that the Kisyński approach can be adapted to empathy...

An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces

M. Poppenberg (1999)

Studia Mathematica

A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces C ( K ) , S ( N ) , B ( R N ) , D L 1 ( N ) , for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

An averaging principle for stochastic evolution equations. II.

Bohdan Maslowski, Jan Seidler, Ivo Vrkoč (1991)

Mathematica Bohemica

In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.

Approximate solution of an inhomogeneous abstract differential equation

Emil Vitásek (2012)

Applications of Mathematics

Recently, we have developed the necessary and sufficient conditions under which a rational function F ( h A ) approximates the semigroup of operators exp ( t A ) generated by an infinitesimal operator A . The present paper extends these results to an inhomogeneous equation u ' ( t ) = A u ( t ) + f ( t ) .

Currently displaying 21 – 40 of 335