Nonlocal semilinear evolution equations without strong compactness: theory and applications

Boundary value problems

Luisa Malaguti³  Irene Benedetti⁴  Valentina Taddei⁶ 

[1] di Modena e Reggio Emilia, Modena, Italy;di Modena e Reggio Emilia, Reggio Emilia, Italy;di Perugia, Perugia, Italy;Dipartimento di Matematica e Informatica, UniversitàDipartimento di Scienze Fisiche, Informatiche e Matematiche, UniversitàDipartimento di Scienze e Metodi dell’Ingegneria, Università

关键词: nonlocal condition;    semilinear evolution equation;    fixed point theorems;    optimal feedback control problem;    diffusion problem;    age-structure population model;   

DOI  :  10.1186/1687-2770-2013-60

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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. MSC:34G25, 34B10, 34B15, 47H04, 28B20, 34H05.

【 授权许可】

CC BY