Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Discrete fragmentation with mass loss

Smith, Ann Louise and Lamb, Wilson and Langer, Matthias and McBride, Adam (2012) Discrete fragmentation with mass loss. Journal of Evolution Equations, 12 (1). pp. 181-201. ISSN 1424-3199

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

We examine an infinite system of ordinary differential equations that models a discrete fragmentation process in which mass loss can occur. The problem is treated as an abstract Cauchy problem, posed in an appropriate Banach space. Perturbation techniques from the theory of semigroups of operators are used to establish the existence and uniqueness of physically meaningful solutions under minimal restrictions on the fragmentation rates. In one particular case an explicit formula for the associated semigroup is obtained and this enables additional properties, such as compactness of the resolvent and analyticity of the semigroup, to be deduced. Another explicit solution of this particular fragmentation problem, in which mass is apparently created from a zero-mass initial state, is also investigated, and the theory of Sobolev towers is used to prove that the solution actually emanates from an initial infinite cluster of unit mass.