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 sanchez(at)iam.uni-bonn(dot)de (Daniel Sánchez-Simón del Pino)
Upcoming
January 30th at 14:15 in SR 2.040 .
Speaker: Dr. Irina Aleksandrova
Title: Delay Lyapunov matrix for linear periodic systems
In this talk, we discuss the role which the delay Lyapunov matrix plays in the stability analysis of linear periodic time delay systems. The delay Lyapunov matrix, appearing in the construction of the Lyapunov functionals with a given derivative for this class of systems, is defined as the solution of a linear matrix hyperbolic PDE with delay satisfying a very specific boundary condition along with the symmetry and periodicity properties. The existence and uniqueness issues as well as the construction of the delay Lyapunov matrix are briefly discussed. As an illustration, we consider a scalar equation with the delay being an integer multiple of the period of the coefficients whose delay Lyapunov matrix (a function in this case) appears to be a periodic solution of the one-dimensional wave equation given on a strip. Based on the fundamental solution of the wave equation, it is possible
to derive the representation formula for the delay Lyapunov function along with the Fredholm integral equation of the second kind for the initial function. We demonstrate that our construction is consistent with the existing theory for a particular case of constant coefficients. This is a joint work with Prof. Juan J. L. Velázquez.
Schedule
October 17
Francesca Pieroni
October 24
No seminar
October 31
No seminar
November 7
Elena Demattè (¡Thesis defense! :))
November 14
Sebastián Flores Sepúlveda
November 21
No seminar
November 28
No seminar
December 05
Prof. Marvin Weidner
December 12
No seminar
December 19
Jaime Fonte Noyola
December 26
No seminar
January 9
No Seminar
January 16
Dr. Eugenia Franco
January 23
No seminar
January 30
Dr. Irina Aleksandrova
Past talks
October 17 at 14:15 in SR 2.040 .
Speaker: Francesca Pieroni (Sapienza Università di Roma)
Title: Random Euclidean Matching for exponentially decaying densities
The Random Euclidean Matching problem is the problem of finding the optimal matching between two families of iid random variables distributed in a d-dimensional domain. Here "optimal" refers to the cost function determined by the sum of the distances between couples of points (elevated to a power p).
In this talk we will first focus on the matching of variables distributed on bounded connected domains. Then we will investigate the case of iid random variables distributed in $\mathbb{R}^d$ according to an exponentially decaying probability density.
November 14 at 14:15 in SR 2.040 .
Speaker: Sebastián Flores Sepúlveda
Title: The moving patch model with fractional Laplacian
In this talk we will discuss a one-dimensional reaction-diffusion equation driven by the fractional Laplacian, given by $u_t + (-\Delta)^s u = f(x-ct, u)$ with $c\in \mathbb{R}$ is a constant. This equation arises as a model for a species subject to a moving environment. We will explain the relation between the long-time behavior of solutions to the parabolic problem, the existence of nontrivial traveling waves and the sign of some generalized principal eigenvalue for an elliptic operator, and detail the main differences between the cases of the fractional and the classical Laplacian.
December 5 at 14:15 in SR 2.040 .
Speaker: Prof. Marvin Weidner
Title: Optimal regularity for kinetic equations in domains
he Boltzmann equation is one of the central equations in statistical mechanics and models the evolution of a gas through particle interactions. In recent years, groundbreaking work by Imbert and Silvestre has led to a conditional regularity theory for periodic solutions of the Boltzmann equation. A major open challenge is whether such a theory can be extended to bounded domains with physically relevant boundary conditions.
As a first step toward understanding the boundary case, in this talk I will discuss the smoothness of solutions to linear kinetic Fokker-Planck equations in domains with specular reflection condition. While the interior regularity of such equations is well understood, their behavior near the boundary has remained open, even in the simplest case of Kolmogorov's equation. I will also mention recent results on other boundary conditions such as diffuse reflection and in-flow.
This talk is based on joint works with Xavier Ros-Oton and Kyeongbae Kim.
December 19 at 14:15 in SR 2.040 .
Speaker: Jaime Fonte Noyola
Title: An analysis of disjoinig pressure in Thin Film flows
The study of viscous thin films provides an interesting case of study for the Navier-Stokes equations since a lubrication approximation leads to a simplification of these. Of particular interest in physical sciences and mathematics is the study of the moving contact lines, since the no slip condition of viscous liquids does not fully describe their behaviour. One of the proposed solutions to this is the study of the disjoining pressure that acts on a liquid film, which leads to a degenerate fourth-order evolution PDE. In this talk we will present the derivation of this equation. We will also discuss the existence and boundedness of smooth positive solutions, as well as analogous results for weak nonnegative solutions. This is based on various works by Andrea Bertozzi and Mary Pugh.
January 16 at 14:15 in SR 2.040 .
Speaker: Dr. Eugenia Franco
Title: Critical lack of detailed balance in kinetic proofreading
In this talk, I will discuss the role of the lack of detailed balance in a class of stochastic kinetic proofreading models. Kinetic proofreading systems were proposed by Hopfield and Ninio in the 70's in order to explain the ability of receptors to distinguish between different ligands with low error rates (strong specificity). We prove the existence of a critical lack of detailed balance that the kinetic proofreading models considered in this talk must have in order to function, i.e. in order to have strong specificity. This is joint work with Juan J. L. Velázquez.
