Global attractor for a class of partial functional differential equations with infinite delay (Q2738673)

The authors consider the partial functional-differential equation with infinite delay NEWLINE\[NEWLINEx'(t)= Ax(t)+f(x_t), \quad t\geq 0,NEWLINE\]NEWLINE with the initial condition \(x_0= \varphi \in {\mathcal B}\), where \(A:D(A)\subset E \to E\) is a closed linear operator with nondense domain, \(E\) is a Banach space, \({\mathcal B}\) is the phase space introduced by \textit{J. K. Hale} and \textit{J. Kato} [Funkc. Ekvacioj, Ser. Int. 21, 11-41 (1978; Zbl 0383.34055)] and \(F:{\mathcal B}\to E\) is a continuous function.NEWLINENEWLINENEWLINEThey provide local and global existence results as well as uniqueness and regularity of the solutions. Moreover, under suitable assumptions, the asymptotic smoothness of the semiflow is obtained and, hence, the existence of a global attractor.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00044].