|Course title||Nonlinear Continuum Mechanics|
|Organizational form of instruction||Lecture + Seminar|
|Level of course||Master|
|Year of study||not specified|
|Number of ECTS credits||4|
|Language of instruction||Czech|
|Status of course||unspecified|
|Form of instruction||Face-to-face|
|Work placements||This is not an internship|
|Recommended optional programme components||None|
A. The language of dynamical systems 1. A summary of linear systems 2. De-motivation: Chaos and the Lorenz attractor 3. Case-study: Driven damped oscillations 4. Relation of non-linear to linear systems: The Hartman-Grobman Theorem 5. Chaos forbidden: The Poincare-Bendixon Theorem B. Fixed-point methods 1. Fixed-point theorems 2. Standard applications 3. BVP for nonlinear ODEs 4. nonlinear PDEs: Classical approach 5. nonlinear PDEs: Modern approach 6. modern approach to nonlinear evolution PDEs. C. Monotonicity methods 1. Monotonicity and the Browder-Minty Theorem 2. Application: The method of lower and upper solutions 3. Pseudo-monotonicity and the Brezis Theorem 4. Application to steady state problems 5. Application to evolution problems
|Learning activities and teaching methods|
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
Understand the language of dynamical systems and solution methods for nonlinear ODEs and PDEs based on fixed-point principles and monotonicity.
Comprehension Understand the mathematical tools of nonlinear partial differential equations.
Classical and modern theory of ODEs and PDEs, Lebesgue's theory, calculus.
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|Assessment methods and criteria|
Oral exam, Written exam
|Study plans that include the course|
|Faculty||Study plan (Version)||Branch of study Category||Recommended year of study||Recommended semester|