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

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].

Cited by in corpus (7)

• Factorization for non-symmetric operators and exponential H-theorem
• A non-conservative Harris ergodic theorem
• Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate
• Exponential relaxation to self-similarity for the superquadratic fragmentation equation
• Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate
• Global stability for the prion equation with general incidence
• Spectral analysis of semigroups and growth-fragmentation equations