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Zeitschrift für Analysis und ihre Anwendungen


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Volume 28, Issue 3, 2009, pp. 295–303
DOI: 10.4171/ZAA/1386

Published online: 2009-09-30

Asymptotic Behavior of Approximate Solutions to Evolution Equations in Banach Spaces

Sergiu Aizicovici[1], Simeon Reich[2] and Alexander J. Zaslavski[3]

(1) Ohio University, Athens, United States
(2) Technion - Israel Institute of Technology, Haifa, Israel
(3) Technion - Israel Institute of Technology, Haifa, Israel

We study evolution equations in Banach spaces governed by a class of mappings associated with continuous descent methods for the minimization of convex functions. In our previous work we showed that for most of these mappings (in the sense of Baire category) the corresponding solutions converged. In the present paper we show that this remains true even for approximate solutions.

Keywords: Complete uniform space, convex function, descent method, generic property, initial value problem

Aizicovici Sergiu, Reich Simeon, Zaslavski Alexander: Asymptotic Behavior of Approximate Solutions to Evolution Equations in Banach Spaces. Z. Anal. Anwend. 28 (2009), 295-303. doi: 10.4171/ZAA/1386