Course title  Nonlinear Continuum Mechanics 

Course code  KMA/NLUM 
Organizational form of instruction  Lecture + Seminar 
Level of course  Master 
Year of study  not specified 
Semester  Summer 
Number of ECTS credits  4 
Language of instruction  Czech 
Status of course  unspecified 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Lecturer(s) 


Course content 
A. The language of dynamical systems 1. A summary of linear systems 2. Demotivation: Chaos and the Lorenz attractor 3. Casestudy: Driven damped oscillations 4. Relation of nonlinear to linear systems: The HartmanGrobman Theorem 5. Chaos forbidden: The PoincareBendixon Theorem B. Fixedpoint methods 1. Fixedpoint 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 BrowderMinty Theorem 2. Application: The method of lower and upper solutions 3. Pseudomonotonicity 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

Learning outcomes 
Understand the language of dynamical systems and solution methods for nonlinear ODEs and PDEs based on fixedpoint principles and monotonicity.
Comprehension Understand the mathematical tools of nonlinear partial differential equations. 
Prerequisites 
Classical and modern theory of ODEs and PDEs, Lebesgue's theory, calculus.
KMA/MK2  or  KMA/MK2A 
Assessment methods and criteria 
Oral exam, Written exam
seminar work 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 
