Nonlocal semilinear evolution equations without strong compactness: theory and applications

作者：Benedetti Irene; Malaguti Luisa; Taddei Valentina^*

来源：Boundary Value Problems, 2013, 2013(1): 60.

DOI：10.1186/1687-2770-2013-60

• nonlocal condition
• semilinear evolution equation
• fixed point theorems
• optimal feedback control problem
• diffusion problem
• age-structure population model

A semilinear multivalued evolution equation is considered in a reflexive Banach space. The nonlinear term has convex, closed, bounded values and a weakly sequentially closed graph when restricted to its second argument. No strong compactness is assumed, neither on the evolution operator generated by the linear part, or on the nonlinear term. A wide family of nonlocal associated boundary value problems is investigated by means of a fixed point technique. Applications are given to an optimal feedback control problem, to a nonlinear hyperbolic integro-differential equation arising in age-structure population models, and to a multipoint boundary value problem associated to a parabolic partial differential equation.

• 出版日期2013