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Lecturer(s)
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Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
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Course content
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Nonlinear ODE, examples. PDE of 2nd order in divergent form. Examples. Variational formulation of boundary problems for equations in divergent form. Calculus of variation: Lagrangian, Euler-Lagrang equation. Koercitivity, weak lower semicontinuity, fundamental theorem of calculus of variation, relation of convexity of Lagrangian and existence of minimum. Fundamental fixed point theorems (Banach, Brower, Schauder, Schaeffer) and their applications to solving of PDE. Method of monotonne operators: fundamental theorem, applications to PDE.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments)
- Home preparation for classes
- 90 hours per semester
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Learning outcomes
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Nonlinear ODE, examples. PDE of 2nd order in divergent form. Examples. Variational formulation of boundary problems for equations in divergent form. Calculus of variation: Lagrangian, Euler-Lagrang equation. Koercitivity, weak lower semicontinuity, fundamental theorem of calculus of variation, relation of convexity of Lagrangian and existence of minimum. Fundamental fixed point theorems (Banach, Brower, Schauder, Schaeffer) and their applications to solving of PDE. Method of monotonne operators: fundamental theorem, applications to PDE.
fundametals of nonlinear diferencial equtions
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Prerequisites
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Passing of lectures in mathematical bachelor study.
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Assessment methods and criteria
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Oral exam, Written exam
Credit: Working out a semestral work. Exam: Written and oral.
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Recommended literature
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S. Fučík, A. Kufner. Nelineární diferenciální rovnice.
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