I will talk about some problems in Vectorial Calculus of Variation in L^\infty. This topic was introduced by Gunnar Aronsson in 1960s in one dimensional case. He first studied the relation between \infty laplacian and the absolute minimisers, where the infinity Laplacian plays a role similar to Euler Lagrange equation. Recently in 2010s Nikos Katzourakis proposed an extension of the Aronsson’s equation to vectorial case (N-dimensions with N\geq 2). In this talk we will discuss the history of the problem, some results in high dimensions with classical solutions and technical challenges of the deriving the “best’’ vectorial \infinity laplacian.

Duvan Cardona (Ghent University, Belgium)

Control theory for diffusion models on compact manifolds

Over the years, in control theory, the null-controllability of diffusion models for (non-local) elliptic pseudo-differential operators has been an open problem. We will discuss the recent progress on it in the case of closed manifolds

Madi Yergaliyev (Al-Farabi Kazakh National University and Institute of Mathematics and Mathematical Modeling, Kazakhstan)

On an inverse problem with an integral overdetermination for the Burgers equation

In the work we consider one inverse problem for the Burgers equation with an integral overdetermination and periodic boundary conditions. In the course of solving the inverse problem, we reduce it to investigation the initial boundary value problem for the loaded Burgers equation. For the latter theorem on its unique solvability in Sobolev classes is proved by the methods of Faedo-Galerkin, a priori estimates and functional analysis. Further, the theorems on the unique solvability of the initial inverse problem are also proved. Graphs of the solution to the initial boundary value problem for the loaded Burgers equation and the desired function of the inverse problem are presented