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A distributional approach to fragmentation equations

Lamb, Wilson and Mcbride, Adam (2011) A distributional approach to fragmentation equations. Communications in Applied Analysis, 15. pp. 511-520. ISSN 1083-2564

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We consider a linear integro-di®erential equation that models multiple fragmentation with inherent mass-loss. A systematic procedure is presented for constructing a space of generalised functions Z0 in which initial-value problems involving singular initial conditions such as the Dirac delta distribution can be analysed. The procedure makes use of results on sun dual semigroups and quasi-equicontinuous semigroups on locally convex spaces. The existence and uniqueness of a distributional solution to an abstract version of the initial-value problem are established for any given initial data u0 in Z0.