Events

In this lecture we will discuss compartmental epidemiological models of infection progression in a space-distributed multi-patch population with a communication between the patches due to the movement of individuals.

We investigate Sobolev and Hardy inequalities, specifically weighted Minerbe’s type estimates, in non compact completeconnected Riemannian manifolds whose geometry is described by an isoperimetric profile. In particular, we assume that the manifold satisfies the p-hyperbolicity property, stated in terms of a necessary integral Dini condition on the isoperimetric profile.

There will be done a review of results about nonnegative solutions of semi-linear equations of diffusion-nonlinear degenerate absorption, which take infinite value on some subsets or all boundary of the domain under consideration: so called very singular and large solutions.

In the period 2007-2014, a number of events related to natural hazards, which caused significant damage, occurred in the South of Russia.

In [1] a similar problem has been solved by probabilistic methods. In my talk, I will speak about an approach to solving this problem based on the non-oscillating WKB method. The difficulty arising in this case is that the representation of the Dirac delta-function in the form of a non-oscillating WKB function is little (let's say) known.

This lecture will provide an overview of recent work on mathematical modeling of viral infection and immune response, carried out at the Research Center for Mathematical Modeling in Biomedicine (Nikol'skii Mathematical Institute, RUDN University). The current work and prospects for the development of this scientific direction will also be discussed.

The interdisciplinary research center "Mathematical Modeling in Biomedicine" was established three years ago at the S. M. Nikol’skii Mathematical Institute, RUDN University. The main research areas of this center include modeling of the cardiovascular system and diseases, infectious diseases and immune response, modeling of cancer diseases, as well as mathematical analysis of models that arise in biomedicine.

For quasilinear partial differential equations and inequalities containing nonlinearities of the Kardar–Parisi–Zhang type (i.e., the scalar square of the gradient and its generalizations), we present a summary of (old and recent) results regarding the stabilization of solutions (for the parabolic and elliptic cases), the blow-up of solutions, and specific phenomena (e.g., the extinction of solutions). Descriptive examples demonstrating the Bitsadze approach (the technique of monotone maps) applied in this research area are provided.