MU03135 Partial Differential Equations II

Mathematical Institute in Opava
Winter 2015
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Prednáška je úvodom do modernej teórie PDR, teórie, ktorá sa zaoberá PDR pre ktoré klasické riešenia neexistujú ( pretože napríklad dáta úlohy nie sú hladké, alebo úlohu riešime na komplikovanej oblasti, alebo ide o úlohy nelineárnu).
Syllabus
  • 1.Elliptic equations. Potentials: volume potential, simple layer potential, double layer potential. Green formulas. Generalized Green formula. Harmonic functions: Dirichlet integral, Gauss integral theorem. Dirichlet problem and Neumann problem. Poisson formula
    2.Elements of distribution theory. Test functions. Decomposition of the unity. Localization. Support. Regular and singular distributions. Operations over distributions. Convolution
    Method of integral transforms. The Fourier transform. The Laplace transform
    3.Modern methods of solving PDEs. Sobolev spaces. Generalized solutions. Lax-Milgram theorem
Literature
    recommended literature
  • V. I. Averbuch. Partial differential equations. MÚ SU, Opava. info
  • J. Franců. Moderní metody řešení diferenciálních rovnic. Brno, 2002. info
  • R. Strichartz. A guide to distribution theory and Fourier transforms. 1994. info
  • M. Renardy, R. C. Rogers. An introduction to partial differential equations. New York, 1993. info
  • C. Zuily. Problems in distributions and partial differential equations. 1988. info
  • D. Gilbarg, N. S. Trudinger. Elliptic partial differential equations of second order. Second edition. Springer, Berlin, 1983. info
  • L. Schwartz. Matematické metody ve fyzice. Státní nakladatelství technické literatury, Prah, 1972. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020.
  • Enrolment Statistics (Winter 2015, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2015/MU03135