TY - JOUR
T1 - Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates
AU - Balagué, D.
AU - Cañizo, J.A.
AU - Gabriel, P.
PY - 2013/6/1
Y1 - 2013/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84877072779&partnerID=8YFLogxK
U2 - 10.3934/krm.2013.6.219
DO - 10.3934/krm.2013.6.219
M3 - Article
AN - SCOPUS:84877072779
SN - 1937-5093
VL - 6
SP - 219
EP - 243
JO - Kinetic and Related Models
JF - Kinetic and Related Models
IS - 2
ER -