Events

Topic: mathematical modelling in biomedicine, speakers: members and collaborators of the center

International scientific conference “Catalysis for a Sustainable World” is an interdisciplinary (within the chemical sciences) event organized on the basis of the RUDN University, aimed at attracting a fairly large number of young scientists (including students and graduate students) from abroad and various regions of the Russian Federation with the purpose of exchange of experience and analysis of modern scientific achievements in catalysis. The format of the school-conference provides plenary reports of outstanding invited scientists.

This work is devoted to the study of a mathematical model which considers the processes that affect the virus concentration u(x,t), taking into account virus mutation, reproduction, and genotype dependent mortality, either natural or determined by an antiviral treatment. Once the conditions for the emergence of virus strains have been established, we study the coexistence of viruses by adding a second equation of virus v(y,t).

The talk will be devoted to the recent results by the author on global solvability, well-posedness, interior regularity and large-time decay of solutions to initial-boundary value problems posed on a half-strip for the Zakahrov-Kuznetsov equation and its modified analogue. A sketch of previous results for problems in other domains will be presented as well.

We will discuss nonexistence results we obtained in the recent years for some nonlinear partial differential equations and inequalities containing fractional powers of the Laplace operator.