Stability and saddle-point property for a linear autonomous functional parabolic equation. (English) Zbl 0606.35081

Milota, Jaroslav

Commentat. Math. Univ. Carol. 27, 87-101 (1986).

From the author’s abstract: A linear parabolic functional differential equation \(\overset\circ u(t)+Au(t)=Lu_ t\) with infinite delay is investigated under assumptions that A is a sectorial operator in a Banach space X and L is a continuous linear operator from a space Y of continuous functions with fading memory norm into X. Values of functions from Y are in the domain of fractional power \(A^{\alpha}\), \(0\leq \alpha <1\). A theorem on stability and the saddle-point property is proved.

Reviewer: N.Jacob

MSC:

35R10	Partial functional-differential equations
34K20	Stability theory of functional-differential equations
34K30	Functional-differential equations in abstract spaces
35G10	Initial value problems for linear higher-order PDEs
35K25	Higher-order parabolic equations

Keywords:

parabolic functional differential equation; infinite delay; sectorial operator; Banach space; fading memory; stability; saddle-point property