Transport theory in PDEs

General data

Course ID:	1000-1M20TT
Erasmus code / ISCED:	11.1 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Transport theory in PDEs
Name in Polish:	Teoria transportu w RRCz
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Prerequisites (description):	(in Polish) Silnie zainteresowanie analizą matematyczną, analiza funkcjonalna.
Full description:	The aim of the lecture is to introduce the theory of the transport equation from the viewpoint of the Partial Differential Equations. The results from the last decade will be in particular interests. The subject is to discuss all properties of the solutions to transport equations and related topics. In the scope we find also analytical theories (from the functional analysis) and applications to systems of PDEs. The main setting will be based on the Lebesgue spaces, but in a natural way we will be supported by the measure theory, too. Content: -- elements of the classical theory; -- the Euler vr. Largangian coordinates; - regular flow; - theory of existence/uniqueness/ununiqueness in the low regularity; - application to the kinetic theory; - application in systems of aggregation and fluid mechanics. Requirements: strong interests in mathematical analysis, functional analysis.
Bibliography:	(in Polish) D. Bresch, P.-E. Jabin: Global weak solutions of PDEs for compressible media: a compactness criterion to cover new physical situations. Shocks, singularities and oscillations in nonlinear optics and fluid mechanics, 33--54, 2017. Crippa, Gianluca; De Lellis, Camillo Estimates and regularity results for the DiPerna-Lions flow. J. Reine Angew. Math. 616 (2008), 15--46. DiPerna, R. J., Lions, P. L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), 511--547. Jabin, Pierre-Emmanuel Critical non-Sobolev regularity for continuity equations with rough velocity fields. J. Differential Equations 260 (2016), no. 5, 4739--4757.
Learning outcomes:	The student distinguishes between transport in Sobolev spaces and public transport
Assessment methods and assessment criteria:	Oral exam

This course is not currently offered.

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