BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

On the Systems of Nonlinear Evolution Equations – Existence and Uniqueness vie Theory of M-matrices

Tuesday 5th November 2024 at 12:30

Abstract. A system of nonlinear evolution equations with strictly monotone operators and perturbations satisfying certain counterpart of one-sided Lipschitz condition is considered. To reach the existence and uniqueness result, a certain remetrization method is proposed based on M-matrices theory and utilizing the Gelfand triple setting, which enables usage of a certain type of relaxed monotonicity. Asymptotic properties of the solution are also investigated by showing that any solution tends to the solution of a stationary problem. The results obtained are illustrated by considering a system of equations involving (q,p)-Laplacians and suitable non-monotone perturbations.

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

The lecture will be given by Dr. Michał Bełdziński,

Institute of Mathematics, Lodz University of Technology, Lodz, Poland

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

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

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

Spectral resolutions for non-self-adjoint convolution operators

Thursday 20th June 2024 at 11:00

Abstract. This talk presents a spectral theory for a class of non-self-adjoint convolution type operators. Particular attention is paid to spectral decomposition (in terms of suitable invariant chains) of the convolution operators under consideration, summing up the extension to them of the classical Schur theory on the triangular decomposition of matrices. It is considered the general case of operators defined on Banach spaces. Applications to the spectral theory of periodic Jacobi type operators that are applicable to mathematics, physics, mathematical physics and others will also be given.

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

THE LECTURE WILL BE GIVEN BY DR. EWELINA ZALOT,

Faculty of Applied Mathematics, AGH University of Krakow, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

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

On Tuesday 30th January City of Brno Councillors honoured leading personalities who, significantly and positively influencing fields of public life, contribute to the city goodwill. Three BUT representatives were among the 13 rewarded personalities. Mathematician Josef Diblík, physicist Ilona Müllerová, and architect Marek Štěpán received the price from the Mayor of the City, Markéta Vaňková.

Professor RNDr. Josef Diblík, DrSc. is among the most distinctive scientists, researchers and teachers at BUT where he has been working since 1980. He was the head of the Department of Mathematics, and Descriptive Geometry at the BUT Faculty of Civil Engineering, working now at the Department of Mathematics of the BUT Faculty of Electrical Engineering and Communication and at BUT Central European Institute of Technology. His research concerns applied mathematics specializing on engineering fields – stability of the solutions to systems modelled by equations of different types, their controllability and stability. He significantly contributes to linking applied mathematics with engineering problems such as systems of automatic control. The results of his research are published in the world’s leading journals. For his scientific results he has been rewarded many times, among others, he is the holder of a M. M. Bogoljubov medal for outstanding results in mathematics.
 

For many years, mathematician Josef Diblík served as the head of the Department of Mathematics and Descriptive Geometry of the BUT Faculty of Civil Engineering. He has been honoured for his contribution to science | Author: Marie Schmerková

Students are reminded,
that it is their duty, rather than their teachers’, to register for a course. Other problems such as those concerning individual study schedules, disabled registration for a mathematics course, etc. should be dealt with in cooperation with RNDr. Rudolf Schwarz, CSc. during his office hours – Wednesday 10.00 – 11.00.

Approved by: Ing Jan Holešovský, Ph.D.,
Head of the Institute of Mathematics and Descriptive Geometry.
Brno dated 1st September 2023.

BUT Faculty of Civil Engineering,
Department of Mathematics and Descriptive Geometry
invites you to a lecture

Conditional Lipschitz shadowing for ordinary differential equations

Tuesday 29th August 2023 at 13:00

Abstract. We introduce the notion of conditional Lipschitz shadowing which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain nonautonomous ordinary differential equations have such a property. The first criterion applies to a semilinear differential equation provided that its linear part is hyperbolic and the nonlinearity is small in a neighborhood of the prescribed set. The second criterion requires that the logarithmic norm of the derivative of the right-hand side with respect to the state variable is uniformly negative in a neighborhood of the prescribed set. The results are applicable to important classes of model equations including the logistic equation, whose conditional shadowing has recently been studied. Several examples are constructed showing that the obtained conditions are optimal.

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. It is supported by the programmes Excellence RP902315002 and PPSŘ RP122314001.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry

Handout