Continuous fragmentation equations in weighted L1 spaces

Tools

Kerr, Lyndsay and Lamb, Wilson and Langer, Matthias; Trostorff, Sascha and Waurick, Marcus, eds. (2026) Continuous fragmentation equations in weighted L1 spaces. In: PDEs, Operator Theory, and Mathematical Physics. Operator Theory: Advances and Applications . Birkhäuser, Cham, Switzerland. ISBN 9783032216076 (In Press)

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Abstract

We investigate an integro-differential equation that models the evolution of fragmenting clusters. We assume cluster size to be a continuous variable and allow for situations in which mass is not necessarily conserved during each fragmentation event. We formulate the initial-value problem as an abstract Cauchy problem (ACP) in an appropriate weighted L1 space, and apply perturbation results to prove that a unique, physically relevant classical solution of the ACP is given by a strongly continuous semigroup for a wide class of initial conditions. Moreover, we show that it is often possible to identify a weighted L1 space in which this semigroup is analytic, leading to the existence of a unique, physically relevant classical solution for all initial conditions belonging to that space. For some specific fragmentation coefficients, we provide examples of weighted L1 spaces where our results can be applied.

ORCID iDs

Kerr, Lyndsay ORCID logoORCID: https://orcid.org/0000-0002-6667-7175, Lamb, Wilson and Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914; Trostorff, Sascha and Waurick, Marcus
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