Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces

Details Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces

2011-02-17

arxiv.org/abs/1102.3661v1

Communications in Applied and Industrial Mathematics, Vol. 1, No. 2, pp. 299-308 (2011)

Mathematics

Analysis of PDEs

Scientific paper

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].

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