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FSI-SDR-AAcad. year: 2023/2024
The course yields overview of modern methods for solving differential equations based on functional analysis. It deals with the following topics: Survey of spaces of functions with integrable derivatives. Linear elliptic equations: the weak and variational formulation of boundary value problems, existence and uniqueness of the solution, approximate solutions and their convergence. Characteristics of the nonlinear problems. Weak and variational formulation of the nonlinear coercive stationary problems, existence of the solution. Application to the selected nonlinear equations of mathematical physics. Introduction to stochastic differential equations.
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