Nonlinear evolution equations in an arbitrary Banach space

This paper proves the existence of an evolution operatorU(t, s)x ₀ corresponding to a weak or generalized solution of the differential equation:du (t)/dt +A (t)u(t) ? f(t), u(s) =x ₀,t ≧ s; the operatorsA(t) are eachm-accretive in a Banach spaceX and, loosely speaking, have an “L¹ modulus of continuity” int. The continuity and differentiability properties ofU(t, s)x₀ are investigated, and some simple examples are presented.