Results 21 to 30 of about 602 (89)
Quasiasymptotic analysis in Colombeau algebra
Journal of Mathematical Analysis and Applications, 2005 The notions of quasiasymptotic and \(S\)-asymptotic behaviour and expansion have been well developed in the spaces of generalized functions (distributions, ultradistributions, hyperfunctions, etc.). The present paper treats the problem how to apply the quasiasymptotics and the \(S\)-asymptotics to the Colombeau algebra.
Pilipović, Stevan, Stojanović, Mirjana
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Natural topologies on Colombeau algebras
Topological Methods in Nonlinear Analysis, 2009 We define natural topologies on the Colombeau algebras which are compatible with the algebraic structure. These topologies reduces do Scarpalezos sharp topologies when restricted. with this we take a positive step towards topological methods of solving P.D. Equations in Colombeau algebras. Applications will appear elsewhere.
Aragona, Jorge +2 more
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Colombeau algebras on a C∞-manifold
Indagationes Mathematicae, 1991 AbstractIn this paper Colombeau's algebra of functions on Rn, containing the distributions, is generalized to a sheaf on a C∞-manifold. The well-known problem of restricting distributions to a submanifold is solved within this framework.
de Roever, J.W. +3 more
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Some Nonlinear Stochastic Cauchy Problems with Generalized Stochastic Processes
International Journal of Analysis, Volume 2016, Issue 1, 2016., 2016 We study some nonlinear stochastic Cauchy problems in the framework of the (C,E,P)‐algebras. We adapt the definitions to this framework. By means of suitable regularizations, we define associated generalized problems. We use our previous results about the wave equation in canonical form to obtain generalized solutions.
Victor Dévoué, Ying Hu
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Compatibility Conditions and the Convolution of Functions and Generalized Functions
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 The paper is a review of certain existence theorems concerning the convolution of functions, distributions, and ultradistributions of Beurling type with supports satisfying suitable compatibility conditions. The fact that some conditions are essential for the existence of the convolution in the discussed spaces follows from earlier results and the ...
Andrzej Kamiński +2 more
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The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each such solution may be represented in a canonical way through its generalized partial derivatives as nearly finite normal lower ...
Jan Harm van der Walt, Svatoslav Stanek
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Further Results on Colombeau Product of Distributions
International Journal of Mathematics and Mathematical Sciences, Volume 2013, Issue 1, 2013., 2013 Results on Colombeau product of distributions x+-r-12/ and x--r-12/ are derived. They are obtained in Colombeau differential algebra 𝒢(R) of generalized functions that contains the space 𝒟′(R) of Schwartz distributions as a subspace and has a notion of “association” that is a faithful generalization of the weak equality in 𝒟′(R).
Biljana Jolevska-Tuneska +2 more
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Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. An abstract stochastic Colombeau algebra is constructed, and solutions in the algebra are studied.
Irina V. Melnikova +2 more
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Step Soliton Generalized Solutions of the Shallow Water Equations
Journal of Applied Mathematics, Volume 2012, Issue 1, 2012., 2012 Generalized solutions of the shallow water equations are obtained. One studies the particular case of a generalized soliton function passing by a variable bottom. We consider a case of discontinuity in bottom depth. We assume that the surface elevation is given by a step soliton which is defined using generalized solutions (Colombeau 1993).
A. C. Alvarez +3 more
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