Scientific Program

The scientific program of the Centre of Applied Mathematics (CAM) is based on the analysis of nonlinear differential equations and systems of differential equations modelling some types of stationary and nonstationary processes. Results and methods of functional analysis concerning the existence, multiplicity and stability of solutions of modelled nonlinear equations are deepened and further developed by CAM. Furthermore, the problems of bifurcations and stability are studied in the case of strongly nonlinear processes which can be described by variational inequalities, and general inclusions respectively, and which are motivated by biological and ecological models. Other analyzed questions concern systems of nonstationary nonlinear differential equations which contain some elliptic operator. They have not been answered satisfactorily yet and can be examined only partially by methods of numerical analysis.

It is necessary to create a team closely connected to the highly professional mathematical institute of the Academy of Science. Such a team should ensure the prospect of the scientific work in the field of nonlinear problems, as well as of studies of applied mathematics at the University of West Bohemia.

The scientific program of the Centre of Applied Mathematics can be divided into the following partial targets:
  • Variational and topological principles and studies of quasilinear problems as a p-Laplacian. The aim of the research is to obtain new information about the solvability of above mentioned problems.
  • Nonclassical variational principles and studies of hybrid and dual problems. The aim of the research is a numerical analysis of convergence and the application of a posteriori estimates of errors of an approximate solution in building and realization of corresponding solvers.
  • Dynamical systems and the analysis of problems of existence, uniqueness or multiplicity of solutions. The main attention is paid to the stability of solutions and to the problems of bifurcation. The research is concentrated to bifurcational phenomena and their numerical modelling.
  • Nonstationary nonlinear problems connected with the problematic of dynamics of liquids and thermodynamics, and in particular with turbulences. The aim of the research is to find numerical approaches to solve these problems, and to provide their theoretical analysis.
  • Degenerate and singular problems for elliptic differential equations. The aim of the research is to apply the theory of weighed Sobolev spaces to get new results in this field.
  • Bifurcation and stability for differential equations and variational inequalities, and inclusions respectively. The aim of the research is - in a cooperation with the part of the team from the Mathematical Institute of the Academy of Science - to complete known results concerning bifurcations and stability of solutions of reaction-diffusion systems with nonstandard boundary conditions described by inequalities and inclusions. This research follows the former cooperation of the Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, and the Mathematical Institute of the Academy of Science of the Czech Republic.

The partial targets stated above are connected by personalities of Pavel Drabek and Milan Kucera, as well as by cooperation with some other members of the Department of Mathematics (e.g. Alois Kufner, Stanislav Mika, Petr Prikryl). This kind of cooperation is necessary since the numerical analysis requires a correct formulation of problems, including the basic information about the qualitative behaviour of the solutions. On the other hand, the theoretical research needs a reasonable stimulation provided by the numerical studies. The intention of the research group is to follow the scheme model - theory - numerical computation.



Scientific program