Seminar “Mathematical model of emergence, competition, and coexistence of virus strains in dependence of virus genotype”
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).
Seminar “Initial-boundary value problems for the two-dimensional Zakharov-Kuznetsov equation and its modifications”
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.
Scientific seminar “On nonexistence of solutions to some nonlinear inequalities with a fractional Laplacian”
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.