Rate of convergence to self-similarity for the fragmentation equation in L1 spaces

Maria J. Caceres (1) , José Alfredo Cañizo (2) , Stéphane Mischler (3)

1 UGR - Departamento de Matematica Aplicada
2 UAB - Departament de Matemàtiques [Barcelona]
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In a recent result by the authors, 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 arXiv : 1006.5523.

Domaines: Equations aux dérivées partielles [math.AP]

Maria J. Caceres, José Alfredo Cañizo, Stéphane Mischler. Rate of convergence to self-similarity for the fragmentation equation in L1 spaces. Communications in Applied and Industrial Mathematics, 2010, 1 (2), pp.299-308. ⟨hal-00659001⟩