Self-similar solutions of fragmentation equations revisited

Abstract

We study the large time behaviour of the mass (size) of particles described by the fragmentation equation with homogeneous breakup kernel. We give necessary and sufficient conditions for the convergence of solutions to the unique self-similar solution.

17 pages

References in corpus (4)

• Substochastic semigroups and densities of piecewise deterministic Markov processes
• Probabilistic aspects of critical growth-fragmentation equations
• Existence of invariant densities for semiflows with jumps
• Time Asymptotics for a Critical Case in Fragmentation and Growth-Fragmentation Equations

Cited by in corpus (3)

• Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate
• On spectral gaps of growth-fragmentation semigroups in higher moment spaces
• Explicit solutions to some fragmentation equations with growth or decay