In a recent result by the authors (ref. ) 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. .
|Number of pages||10|
|Journal||Communications in Applied and Industrial Mathematics|
|Publication status||Published - 1 Feb 2011|