In this talk we address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the ...
Quantum simulators were originally proposed to be helpful for simulating one partial differential equation (PDE) in particular – Schrodinger’s equation. If quantum simulators can be useful for simulat...
This talk is devoted to the modeling and stability of multi-lane traffic flow in both microscopic and macroscopic frameworks. Firstly, we explore the dynamics of lane changing in microscopic variables...
The talk concerns the ongoing development of a non-standard model of continuum mechanics, originally due to Godunov, Peshkov, and Romenski (GPR), and its numerical approximation in Finite Volume and D...
A classic yet delicate fact of Morse theory states that the unstable manifolds of a Morse-Smale gradient-flow on a closed manifold M are the open cells of a CW-decomposition of M. I will describe a se...
In the common practice of the method-of-lines (MOL) approach for discretizing a time-dependent partial differential equation (PDE), one first applies spatial discretization to convert the PDE into an ...
The first part of the talk is dedicated to the derivation on an advection-diffusion equation in two dimensions from a system of one dimensional hyperbolic PDEs modeling the macroscopic behavior of mul...
We consider general two-dimensional autonomous velocity fields and prove that their mixing and dissipation features are limited to algebraic rates. As an application, we consider a standard cellular f...
Fractional derivatives, a widely recognized mathematical tool, have gained considerable attention in recent decades owing to their non-local behavior, particularly suitable for capturing anomalous dif...
We will consider a type of cooperative nonlinear elliptic system in R^N. The interest of this problem is based on the presence of Sobolev or Sobolev-Hardy critical power nonlinearities and a nonlinear...
We consider maps between spheres \(S^n\) to \(S^\ell\) that minimize the Sobolev-space energy \(W^{s,n/s}\) for some \(s \in (0,1)\) in a given homotopy class. The basic question is: in which homotopy...
Society's ever-increasing integration of autonomous systems in day-to-day life has simultaneously brought forth concerns as to how their safety and reliability can be verified. To this end, reachable ...
