Abstract
In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted \L^2\ spaces of the operator defining the time evolution. In the present work we prove that there is also a spectral gap in weighted \L^1\ spaces, thus extending exponential convergence to a larger set of initial conditions. The main tool is an extension result in ref. [4].
Original language | English |
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Pages (from-to) | 299-308 |
Number of pages | 10 |
Journal | Communications in Applied and Industrial Mathematics |
Volume | 1 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Feb 2011 |