Local and global solutions of well-posed integrated Cauchy problems
In this paper we study the local well-posed integrated Cauchy problem, v 0 (t) = Av(t) + t fi i(fi + 1) x; v(0) = 0; t 2 [0;•); with • > 0, fi ‚ 0, and x 2 X where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in fi. The global case (• = 1) is also treated in detail. Growths of solutions are given in both cases.