Faculty of Natural and Agricultural Sciences
Department of Mathematics and Applied Mathematics
Partial differential equations, their numerical analysis and mathematical modelling
Partial, ordinary differential equations and stochastic partial differential equations with special attention to mathematical models in science and engineering. The research covers: Function spaces (distributions, Sobolev spaces, etc); existence, uniqueness, regularity and singularity properties of solutions, singularly perturbed problems; numerical treatment by finite element, finite difference and boundary element methods; dynamical systems; interval methods; modification of mathematical models; fluid mechanics; mathematical biology with emphasis on epidemiology.
The study of dense singularities of solutions of nonlinear partial differential equations with emphasis on Lie semigroups of noninvertible transformations of solutions; abstract differential geometry of algebras of generalised functions and de Rham cohomology; space-time foam structures with dense singularities.
Homogenization of elliptic and evolution problems.
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