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Modelling and Products of Singularities in Colombeau's Algebra
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B. Damyanov
Published/Copyright:
June 9, 2010
Abstract
Modelling of singularities given by discontinuous functions or Schwartz distributions by means of generalized functions of Colombeau has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Moreover, we evaluate various products of singularity-modelling generalized functions whenever the result admits an associated distribution.
Key words and phrases.: Colombeau's algebra; singular products of distributions
Received: 2006-05-08
Revised: 2007-04-18
Published Online: 2010-06-09
Published in Print: 2008-June
© Heldermann Verlag
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Articles in the same Issue
- Finite Partitions of Topological Groups into Congruent Thick Subsets
- Derivatives of Markov Kernels and Their Jordan Decomposition
- Sufficiency and Duality in Control Problems with Generalized Invexity
- Koebe Domains for the Classes of Functions with Ranges Included in Given Sets
- Upper and Lower Solutions Method for Fourth-Order Periodic Boundary Value Problems
- Efficiency and Duality for Generalized Convex Multiobjective Programming
- General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces
- Modelling and Products of Singularities in Colombeau's Algebra
- Set Differential Equations in Fréchet Spaces
- Positive Solutions for a Class of Nonresonant m-Point Boundary Value Problems
- Second Order Duality in Multiobjective Programming
