Properties of solutions of ordinary differential equations in banach space

This analysis concerns the study of equations of the form Lu = 1 dui dt - Au = 0 for functions u(t) with values in some Banach space, as well as inhomogeneous equations Lu = f and ligh ly perturbed equations, with the main emphasis on the behavior of solutions a t + . Treated are equations for which the initial value probl (prescribing u at some value of t) is not necessarily well posed. Particularly consi ered are equations arising from partial differential equations in a cylinder (with t axis along the g nerator) which may be elliptic, and for which, therefore the initial value problem is indeed not well posed. The operator A then represents a partial differential operator in the variables in the base of the cylinder. ( ut or)