Abstract
The aim of this note is to improve and complete the estimates given in our paper, Arch. Ration. Mech. Anal. 82, 13-25 (1983). We deal with the problem as introduced by M. E. Gurtin and R. C. MacCamy, ibid. 54, 281-300 (1974), that is to say, we are looking for a function ρ(a,t) satisfying:
ρ a (a,t)+ρ t (a,t)+μ(a,t,P(t))ρ(a,t)=0 for a,t>0,
ρ (0,t)=∫ 0 +∞ β(a,t,P(t))ρ(a,t)da, t>0, ρ(a,0)=φ(a), a>0, where P(t)=∫ 0 +∞ ρ(a,t)da.