BUT Faculty of Civil Engineering,

Department of Mathematics and Descriptive Geometry

invites you to a lecture

### Shadowing, Hyers-Ulam stability and hyperbolicity for nonautonomous linear delay differential equations

**Wednesday 28th August 2024 at 13:00**

**Abstract.** It is known that hyperbolic nonautonomous linear delay differential equations in finite dimensional spaces are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this talk, we show the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the uniform boundedness assumption will be shown by an example.

This is a joint work with Professors Lucas Backes (Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil) and Davor Dragičević (University of Rijeka, Rijeka, Croatia).

**At the department meeting room (2**^{nd} floor Z205), Žižkova 17.

### THE LECTURE WILL BE GIVEN BY PROF. MIHÁLY PITUK,

*Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary*

The lecture is intended for all those interested in these problems.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout