Abstract
We are concerned with the long-time behavior of the growth-fragmentation equation. We prove fine estimates on the principal eigenfunctions of the growth-fragmentation operator, giving their first-order behavior close to 0 and +∞. Using these estimates we prove a spectral gap result by following the technique in [1], which implies that solutions decay to the equilibrium exponentially fast. The growth and fragmentation coefficients we consider are quite general, essentially only assumed to behave asymptotically like power laws. © American Institute of Mathematical Sciences.
Original language | English |
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Pages (from-to) | 219-243 |
Journal | Kinetic and Related Models |
Volume | 6 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jun 2013 |
Keywords
- Eigenvalue problem
- Entropy
- Exponential convergence
- Fragmentation
- Growth
- Long-time behavior