The seminar takes place on Fridays, at 14:15 in SR 2.040.
Mailing List
In order to receive e-mails about the Group seminar, please subscribe to the mailing list or send a short e-mail to cristian(at)iam.uni-bonn(dot)de (Iulia Cristian) or sanchez(at)iam.uni-bonn(dot)de (Daniel Sánchez-Simón del Pino)
Title: Dynamics and qualitative analysis of photosynthetic reactions
In this talk, a mathematical model of the Calvin cycle, a fundamental chemical reaction network in photosynthesis, is explored. By incorporating ATP diffusion, the model is formulated as a system of reaction-diffusion equations. Through rigorous mathematical analysis, we demonstrate the existence of multiple spatially inhomogeneous positive steady states under appropriate parameter settings. Furthermore, it is shown that all positive steady states - homogeneous or inhomogeneous - are nonlinearly unstable, with the exception of a trivial steady state where only ATP has a non-zero concentration. In the spatially homogeneous scenario, linearisation shows that certain steady states have complex eigenvalues, suggesting oscillatory dynamics. Numerical simulations highlight temporal variations in concentrations, showing non-monotonic behaviour over time.
Schedule
October 18
Juan Velázquez
October 25
Iulia's defense ♥
November 01
No seminar
November 08
No seminar
November 15
No Seminar
November 22
Jens Scholten
November 29
Elena Demattè
December 06
Iulia Cristian
December 13
Dimitri Cobb
December 20
TBA
December 27
No seminar
January 10
No seminar
January 17
Burcu Gürbüz
January 24
No seminar
January 31
TBA
Past talks
Friday October 18,Room 2.040 at 14:15
First talk ♥
Title: Mathematical theory for multi-dimensional coagulation models
TBA
Friday November 22
Speaker: Jens Scholten
Title: Understanding the Phase Transition in the 2D Becker-Döring Model
The Becker-Döring equations are the simplest discrete coagulation-fragmentation model, where the cluster interaction only occurs through the monomers. Nonetheless, they are able to describe the phase transition of the underlying physical system and offer a rich mathematical study. We consider a straightforward extension, where clusters are built from two different types of monomers. The added dimension introduces surprising amounts of complexity both physically and mathematically. We investigate the resulting phase transition and propose a rigorous approach via an entropy-entropy dissipation estimate.
Friday November 29
Speaker: Elena Demattè
Title: Equilibrium and Non-Equilibrium diffusion approximation for the Radiative Transfer Equation
In this talk we study the distribution of the temperature within a body where the heat is transported only by radiation. We consider the situation where both emission-absorption and scattering take place. We study the initial boundary value problem given by the Radiative Transfer Equation on a convex domain in the diffusion approximation regime, i.e. when the mean free path of the photons tends to zero. Using the method of matched asymptotic expansions we will derive the limit problems and the boundary layer equations for all scaling limit regimes and we will classify them as equilibrium or non-equilibrium diffusion approximations. This is a joint work with Juan J. L. Velázquez.
Friday December 06
Speaker: Iulia Cristian
Title: Derivation of the diagonal kernel from a spatially
inhomogeneous coagulation model
In a previous work together with Barbara and Juan, we proved local in time existence of mass-conserving solutions for a coagulation model describing the sedimentation of particles. In order to obtain some insight into how to prove global existence of solutions, we modified the model, allowing a fast sedimentation speed. For very fast sedimentation speed, we obtain in the limit a coagulation equation in which only particles of the same size interact (i.e., with diagonal kernel). This establishes a clear connection between our multi-dimensional model and its one-dimensional counterpart.
Title: Global existence and uniqueness of unbounded solutions in the 2D
Euler Equations
In this talk, we will study unbounded solutions of the incompressible
Euler equations in two dimensions of space. The main interest of these
solutions is that the usual function spaces in which solutions are
defined
(for example based on finite energy conditions like $L^2$ or $H^s$) are
not compatible with the symmetries of the problem, namely Galileo
invariance and scaling transformation. In addition, many real world
problems naturally involve infinite energy solutions, typically in
geophysics.
After presenting the problem and giving an overview of previous results,
we will state our result: existence and uniqueness of global Yudovich
solutions under a certain sublinear growth assumption of the initial
data.
The proof is based on an integral decomposition of the pressure and
local
energy balance, leading to global estimates in local Morrey spaces.
This work was done in collaboration with Herbert Koch (Universität
Bonn).
