Nonlinear evolution equations in an arbitrary Banach space
Copyright policy )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.
- University of Kentucky United States
Differential equations in abstract spaces, Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions), Equations involving nonlinear operators (general)
Differential equations in abstract spaces, Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions), Equations involving nonlinear operators (general)
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