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Poslední úprava: doc. Mgr. Petr Kaplický, Ph.D. (07.01.2019)
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Poslední úprava: prof. Mgr. Milan Pokorný, Ph.D., DSc. (07.02.2018)
Exercises: the students are supposed to solve homeworks (written). The deadlines for each set of homework will be announced at least one week in advance. To obtain credits, 30% of the maximal number of points are required. Additionally, at least one oral presentation of a problem from the list available on the web page is required. According to POS, Art. 8, Par. 2 it is not possible to repeat this.
The credit from the exercices is required to participate at the exam.
Exam: written part (based mostly on the material discussed at the exercises and contained in the written homeworks; very basic knowledge from the lectures is also expected); in order to proceed to the oral part, the students must pass the written exam
oral part (based mostly on the material presented during lectures).
Most recommended sources are the book PDE's by L.C. Evans and Lecture notes which will be available on the web page. |
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Poslední úprava: doc. RNDr. Miroslav Bulíček, Ph.D. (11.09.2013)
L. C. Evans: Partial Differential Equations, AMS, 2010. E. Zeidler: Nonlinear Functional Analysis and its Applications II/A, (Chapters 23 and 24), Springer, 1990. |
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Poslední úprava: prof. Mgr. Milan Pokorný, Ph.D., DSc. (07.02.2018)
The credit from the exercises is required to to be allowed to participate at the exam.
The exam will have written part (based on problems studied at the exercises) and oral part (based on material from lectures). In order to proceed to the oral part, the student must pass the written exam. Indeed, everything is combined together and it does not mean that part of the knowledge from the exercises cannot be required at the oral exam. The exercises will be available on the webpage, the lectures are either covered by the material of the book PDE's aby L.C. Evans or by the Lecture notes. All this required theoretical material will be covered at the lectures. |
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Poslední úprava: doc. Mgr. Petr Kaplický, Ph.D. (07.01.2019)
Sobolevovy prostory: věty o vnoření, věty o stopách (s důkazy) Nelineární skalární eliptické rovnice 2. řádu: slabá formulace, existence a jednoznačnost řešení, metoda monotónních operátorů, princip maxima, regularita Úvod do variačního počtu: základní věta variačního počtu, slabá polospojitost konvexních funkcionálů, souvislost s eliptickými rovnicemi (Sobolev-) Bochnerovy prostory: definice a základní vlastnosti, věty o spojitém a kompaktním (Aubin-Lions) vnoření (s důkazy) Teorie semigrup: věta Hille-Yosidova, aplikace na lineární parabolické a hyperbolické problémy. Nelineární parabolické rovnice 2. řádu: existence, jednoznačnost a regularita slabého řešení. |