Events

An inhomogeneous boundary value problem with mixed boundary conditions for the Laplace equation in a domain representing a perturbation of a rectangle in which one of its sides is replaced by some (irregular) curve is considered.

We study a problem of damping a control system described by functional-differential equations of natural order n and neutral type with non-smooth complex coefficients on an arbitrary tree with global delay. The latter means that the delay propagates through internal vertices of the tree.

By expanding the concept of solutions, it was possible to find a proof of sufficiently general theorems of the existence of generalized solutions to systems of two conservation laws (one spatial variable), however, the developed technique as a whole cannot be extended even to systems of three conservation laws with one spatial variable.

Agranovich and Vishik constructed a theory of elliptic boundary value problems depending on a parameter p. This theory plays an important role in the study of many classes of differential equations and their applications (for example, in the case of equations on manifolds with singularities). We report about an analogue of this theory in the case of boundary value problems for pseudodifferential operators. As applications, we will obtain trace asymptotics for elliptic problems with a parameter as p tends to infinity and define eta-invariants for elliptic problems with a parameter.

Well-known results on the boundedness of the classical Riesz potential in lo-cal Morrey-type spaces are generalized to the case of integral operators of Riesz type, in which the power function is replaced by a general function that satisfies certain conditions. For some values of numerical parameters characterizing local Morrey-type spaces, necessary and sufficient conditions for functional parameters are obtained that ensure the boundedness of such operators from one general local Morrey-type space to another.

In this lecture we will present an overview of recent works on mathematical modelling of respiratory viral infections. We will begin with the investigation of infection progression in cell cultures and in tissues of human body.

We establish nonexistence of different types of solutions for some semilinear elliptic inequalities with a transformed argument in a half-space. The proofs are based on the test function method.

We Derive Einstein model of Brownian Motion with Schematic’s in form of system of PDE. We incorporate Einstein’s method of Brownian motion to deduce the chemotactic model exhibiting a traveling band. To our knowledge this was the first time that Einstein’s method has been used to motivate equations describing the mutual interaction of the chemotactic system.

The talk is devoted to the presentation of the results of the investigation of motion of non-potential systems with an infinite number of degrees of freedom, which, on the one hand, is a further development of classical mechanics, and on the other – allows us, as a very special case, to investigate the motion of systems with a finite number of degrees of freedom.

We will discuss two projects: bThe movement of the living organism in a band form towards the presence of chemical substrates based on a system of the PDE.

The talk will start with a survey of various constructions of GMC. We shall then propose a general method for constructing exponentials of random fields and establish convergence to the GMc of random entire functions naturally assigned to the sine-process.

The report examines the inverse problem of finance, which consists of constructing (calibrating) a volatility function using available financial data. An analytical approach to solving the problem is the Dupire formula, which allows to construct a volatility function for given option prices.