Results 41 to 50 of about 602 (89)
SOME RESULTS ON COLOMBEAU PRODUCT OF DISTRIBUTIONS [PDF]
, 2012 In this paper some results on singular products of distributions are derived. The results are obtained in Colombeau algebra of generalized functions, which is most relevant algebraic construction for tackling nonlinear problems of Schwartz ...
JOLEVSKA-TUNESKA, BILJANA +1 more
core
Kernel Theorems in Spaces of Tempered Generalized Functions
, 2006 In analogy to the classical isomorphism between $\mathcal{L}(\mathcal{S}(\mathbb{R}^{n}) ,\mathcal{S}^{\prime}(\mathbb{R}^{m}) ) $ and $\mathcal{S}^{\prime}(\mathbb{R}^{n+m}) $, we show that a large class of moderate linear mappings acting between the ...
ANTOINE DELCROIX +10 more
core +1 more source
Generalized Solutions of a Nonlinear Parabolic Equation with Generalized Functions as Initial Data
, 2008 In \cite{bf} Br\'ezis and Friedman prove that certain nonlinear parabolic equations, with the $\delta$-measure as initial data, have no solution. However in \cite{cl} Colombeau and Langlais prove that these equations have a unique solution even if the ...
Aragona, Jorge +2 more
core +1 more source
Regularity theory in Colombeau algebras
Bulletin: Classe des sciences mathematiques et natturalles, 2006 This paper introduces and discusses various notions of regularity of solutions to partial differential equations in Colombeau algebras. The aim is to suggest a number of approaches that allow to extend the regularity theory to nonlinear equations. A relation with the notion of delta waves is observed.
openaire +2 more sources
Pseudodifferential operators with generalized symbols and regularity theory
Electronic Journal of Differential Equations, 2005 We study pseudodifferential operators with amplitudes $a_varepsilon (x,xi)$ depending on a singular parameter $varepsilon o 0$ with asymptotic properties measured by different scales.
Claudia Garetto +2 more
doaj
Local regularity in non-linear generalized functions [PDF]
, 2013 In this review article we present regularity properties of generalized functions which are useful in the analysis of non-linear problems. It is shown that Schwartz distributions embedded into our new spaces of generalized functions, with additional ...
Pilipovic, Stevan +2 more
core +3 more sources
Microlocal Asymptotic Analysis in Algebras of Generalized Functions
, 2007 We introduce a new type of local and microlocal asymptotic analysis in algebras of generalized functions, based on the presheaf properties of those algebras and on the properties of their elements with respect to a regularizing parameter. Contrary to the
Delcroix, Antoine +2 more
core +2 more sources
NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA
, 2018 In this paper we introduce an approach to fractional derivatives involving singularities based on the theory of algebras of generalized functions in the Colombeau algebra G, using new denition of fractional derivative called conformable fractional derivative introduced by the authors Khalil et al. in ([8]).
MELLİANİ, Said +3 more
openaire +4 more sources
Geodesic completeness of generalized space-times
, 2015 We define the notion of geodesic completeness for semi-Riemannian metrics of low regularity in the framework of the geometric theory of generalized functions.
Steinbauer, Roland, Sämann, Clemens
core +1 more source