For the English version of the introduction click here
A BME Matematika Intézet Analízis és Differenciálegyenletek Tanszékének közös Alkalmazott Analízis Szemináriuma 2016. őszén indult Faragó István (Differenciálegyenletek Tanszék) kezdeményezésére az MTA-ELTE Numerikus Analízis és Nagy Hálózatok Kutatócsoporttal együttműködésben. A szeminárium célja, hogy elősegítse egy alkalmazott analízissel (funkcionálanalízis, differenciálegyenletek, numerikus módszerek) foglalkozó kutatói kör kialakítását az intézeten belül. A szemináriummal fórumot szeretnénk biztosítani az alkalmazott analízissel foglalkozó matematikusok és az analízist alkalmazó kutatók számára az együtt gondolkodásra. További cél az érdeklődő hallgatók (MSc, PhD) bevonása a kutatói munkába.
Szemináriumunk 2017-től felvette a Farkas Miklós Alkalmazott Analízis Szeminárium nevet. Ezzel szeretnénk emléket állítani egyetemünk egykori tanszékvezető matematikaprofesszorának, aki elindította egyetemünkön a matematikus-mérnök képzést, és a stabilitáselmélet valamint a biomatematika terén elért jelentős tudományos eredményeivel ill. könyveivel nagyban hozzájárult az alkalmazott matematika erősödéséhez.
A covid járvány miatt három évig szünetelt a szeminárium. 2023. szeptemberétől indult újra a korábban említett szervezetek utódjainak (BME Analízis és Operációkutatás Tanszék, HUN-REN-ELTE Numerikus Analízis és Nagy Hálózatok Kutatócsoport) szervezésében.
The talks are in English on a regular basis. / Az előadásokat angol nyelven tartjuk.
Organizers / Szervezők: 
Faragó István1,2,3, 
Karátson János1,2,3 ,
Horváth Róbert1,3 ,
Mincsovics Miklós1,3 , 
Svantnerné Sebestyén Gabriella1,3 (1BME, 2ELTE, 3HUN-REN-ELTE NUMNET)
Tentative program of the semester: 14 November (Giuseppe Habib, BME), 28 November - Tamás Pfeil (ELTE), 5 December - Research reports of PhD students
Next seminar: 7 November, Thursday, 10:15, BME H306
György Károlyi (Department of Nuclear Techniques, BME)
Dissipative dynamical systems, or, the transient charm of decay
In undriven dissipative systems all motion decays since dissipation continually decreases the available mechanical energy. Chaotic motion can only show up transiently. Traditional transient chaos is, however, caused by the presence of an infinity of unstable orbits. In the lack of these, chaos in undriven dissipative systems is of another type: it is termed doubly transient chaos as the strength of transient chaos is diminishing in time, and ceases asymptotically. To characterize the behavior of such systems, the snapshot view has been suggested, but it does not lead to a clear characterization of e.g. the fractality of the boundary between the basins of attraction. We suggest that a view based on equal energy levels might be a better choice.
Previous seminars
17 October 2024
Beatrix Oroszi (Centre for Epidemiology and Surveillance, Semmelweis University)
Epidemiology of communicable diseases: dynamics of disease transmission and epidemic control from the perspective of epidemic modelling
In this interactive seminar, we will examine the epidemiological aspects that are integral to the development of models, as well as the epidemiological studies and other routine data collections that can provide critical input parameters. It is essential to gain an understanding of the limitations of such data collections, which will be illustrated by real-world examples. The conditions for the applicability of epidemiological models to public health decision making will then be discussed.
These issues will be explored through the lens of a realistic modelling example of a hypothetical but plausible pandemic emergency caused by a human-to-human respiratory virus. This will provide a context for understanding the theoretical underpinnings of epidemiology in mathematical modelling. At the end of the seminar, we will present our imaginary decision-makers with evidence-based answers to questions about epidemiological interventions in the example. We will recognise that, in certain circumstances, epidemiological models can inform specific decisions that have a significant impact on people's lives. We will therefore examine in detail the specific limitations of the epidemiological model and its outputs, and propose strategies to improve the quality of model outputs.
3 October 2024
Miklós Mincsovics (BME, Department of Analysis and Operations Research)
What makes a good student project?
This is the question we explore in the topic of differential equations and numerical methods. After some introductory thoughts, we will dive deeper into two possible projects: modeling addiction, and modeling the motion of a glider. We will investigate them primarily from an educational point of view, but we will also look at the results achieved so far as research.
19 September 2024
Csaba Farkas (Sapientia - Hungarian University of Transylvania, Department of Mathematics-Informatics)
Compact Sobolev embeddings on non-compact manifolds with applications
In this talk, we collect recent achievements obtained in the theory of geometric analysis, by exploiting elements from the calculus of variations, partial differential equations, Riemann-Finsler geometry and group theory. First, for a given complete non-compact Riemannian manifold (M, g) with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries G of (M, g) that characterizes the coerciveness of G in the sense of Skrzypczak and Tintarev (Arch Math 101(3): 259--268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). Then we give some applications for such results, first, we investigate the existence of multiple solutions for a low-dimensional Dirichlet eigenvalue problem with non-standard growth on a Randers space. Variational techniques, depending in particular on a minimax theorem and the previous compact embeddings, are employed to establish the existence of multiple group invariant solutions. After that, we deal with a quasilinear elliptic equation involving a critical Sobolev exponent on non-compact Randers spaces. Under very general assumptions on the perturbation, we prove the existence of a non-trivial solution. The approach is based on the direct methods of the calculus of variations. We end this talk with the multiplicity of singular fourth-order Schrödinger equation on Hadamard manifolds.
Presentations in 2023/24, 2019/20, 2018/19, 2017/18, 2016/17