Since April 2021, I have been a PhD student under the supervision of Prof. Dr. Juan J. L. Velázquez.
Previously, I earned my master's degree here in Bonn and my bachelor's degree at University of Bucharest.

In this work, we study a particular system of coagulation equations characterized by two values, namely volume $v$ and surface area $a$. Compared to the standard one-dimensional models, this model incorporates additional information about the geometry of the particles. We describe the coagulation process as a combination between collision and fusion of particles. We prove that we are able to recover the standard one-dimensional coagulation model when fusion happens quickly and that we are able to recover an equation in which particles interact and form a ramified-like system in time when fusion happens slowly.

In this paper we study a class of coagulation equations including a source term that injects in the system clusters of size of order one. The coagulation kernel is homogeneous, of homogeneity $\gamma<1$, such that $K(x,y)$ is approximately $x^{\gamma+\lambda}y^{-\lambda}$, when $x$ is larger than $y$. We restrict the analysis to the case $\gamma+2\lambda\geq 1$. In this range of exponents, the transport of mass toward infinity is driven by collisions between particles of different sizes. This is in contrast with the case when $\gamma+2\lambda<1$. In that case, the transport of mass toward infinity is due to the collision between particles of comparable sizes. In the case $\gamma+2\lambda\geq 1$, the interaction between particles of different sizes leads to an additional transport term in the coagulation equation that approximates the solution of the original coagulation equation with injection for large times. We prove the existence of a class of self-similar solutions for suitable choices of $\gamma$ and $\lambda$ for this class of coagulation equations with transport. We prove that for the complementary case such self-similar solutions do not exist.

In this work, we study the long time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision and fusion of particles. During the collision stage, the two particles merge at a contact point. The newly formed particle has volume and area equal to the sum of the respective quantities of the two colliding particles. After collision, the fusion phase begins and during it the geometry of the interacting particles is modified in such a way that the volume of the total system is preserved and the surface area is reduced. During their evolution, the particles must satisfy the isoperimetric inequality. Therefore, the distribution of particles in the volume and area space is supported in the region where $a\geq (36\pi)^{\frac{1}{3}}v^{\frac{2}{3}}$. We assume the coagulation kernel has a weak dependence on the area variable. We prove existence of self-similar profiles for some choices of the functions describing the fusion rate for which the particles have a shape that is close to spherical. On the other hand, for other fusion mechanisms, we show that the particle distribution describes a system of ramified-like particles.

Seminars

I help with the organization of the Graduate Seminar on PDE in the Sciences (Group PDE) and of the Oberseminar Analysis (OS Analysis).

BIGS, Hausdorff Scholarship Hausdorff doctoral position (April 2021 -- Present)

DAAD, Study Scholarship for Graduates of All Disciplines Initial period plus One-off study completion grant (2018 -- 2021)

Study Scholarship Scholarship from Superior Normal School of Bucharest (SNSB) for students in the preparatory cycle (2017 -- 2018)

Study Scholarship Scholarship awarded to students with a perfect GPA, University of Bucharest, Faculty of Mathematics and Computer Science (2016 -- 2018)

News

Prof. Dr. Karl-Theodor Sturm has been elected into the Academia Europaea. (28.06.2022)

Florian Schweiger erhielt den Hausdorff-Gedächtnispreis 2021 der Fachgruppe Mathematik für die beste Dissertation. Er fertigte die Dissertation unter der Betreuung von Prof. Stefan Müller an. Unter anderen wurde Vanessa Ryborz mit einem Preis der Bonner Mathematischen Gesellschaft für ihre von Prof. Sergio Conti betreute Bachelorarbeit ausgezeichnet. (18.01.2022)

Prof. Dr. Sergio Albeverio has been elected into the Academia Europaea and the Accademia Nazionale dei Lincei (more; 02.12.2021).

Der SFB 1060 Die Mathematik der emergenten Effekte hat eine dritte Förderperiode erhalten. (26.11.20)

Herr Dr. Richard Höfer erhielt den Hausdorff-Gedächtnispreis 2019 der Fachgruppe Mathematik für die beste Disseration. Betreut wurde die Arbeit von Prof. J. Velázquez (29.01.2020).