Syllabus
Basic theorems from the theory of monotone and potential operators.
Nonlinear differential equations in divergent form.
Carathéodory's growth conditions, Nemycky operators. Variational methods and aplication of theory of monotone and potential operator, proof of existence of solution.
Numerical solution of nonlinear differential equations using the finite element method.
Annotation
The subject is the solution of nonlinear differential equations in divergence form, the definition of weak solutions, theorems dealing with the existence and uniqueness of the solution using the theory of monotone operators, numerical solution using finite element methods including the discretization and solution of the arising algebraic equations.