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E. A. Nigsch (2017)
Commentationes Mathematicae Universitatis Carolinae
We adapt a nonlinear version of Peetre's theorem on local operators in order to investigate representatives of nonlinear generalized functions occurring in the theory of full Colombeau algebras.
Damyanov, Blagovest P. (2013)
Mathematica Balkanica New Series
MSC 2010: 46F30, 46F10Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of Colombeau that model such singularities. Moreover, we evaluate some products of singularity-modelling generalized functions whenever the result admits an associated distribution.
Victor Dévoué (2007)
Nedeljkov, M., Pilipović, S. (2002)
Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques
M. Nedeljkov, S. Pilipović (2002)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Jiří Jelínek (2004)
Commentationes Mathematicae Universitatis Carolinae
Equivalent definitions of two diffeomorphism invariant Colombeau algebras introduced in [7] and [5] (Grosser et al.) are listed and some new equivalent definitions are presented. The paper can be treated as tools for proving in [8] the equality of both algebras.
Jan Ligęza, Milan Tvrdý (1999)
Mathematica Bohemica
From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra of generalized real numbers. It is worth mentioning that the algebra is not a field.
Jiří Jelínek, Dalibor Pražák (2009)
Commentationes Mathematicae Universitatis Carolinae
A generalized concept of sign is introduced in the context of Colombeau algebras. It extends the sign of the point-value in the case of sufficiently regular functions. This concept of generalized sign is then used to characterize the entropy condition for discontinuous solutions of scalar conservation laws.
Jan Ligęza (2002)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Joseph, Kayyunnapara Thomas (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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