MU03035 Partial Differential Equations II

Mathematical Institute in Opava
Winter 2017
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jana Kopfová, Ph.D. (lecturer)
doc. RNDr. Jana Kopfová, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Jana Kopfová, Ph.D.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU02037 Partial Differential Equations
Course Enrolment Limitations
The course is offered to students of any study field.
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 úlohu nelineárnu).
Syllabus
  • 1.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.
    2.Elliptic equations. Potentials: volume potential, simple layer potential, double layer potential. Green formulas. Generalized Green formula. Harmonic functions. Dirichlet problem and Neumann problem.
    Poisson formula. Maximum principle
    3.Modern methods of solving PDEs. Sobolev spaces. Sobolev imbeddings Theorems. Generalized solutions. Lax-Milgram theorem. Weak and variational formulation.
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 1997, Summer 1998, Winter 1998, Summer 1999, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2018, Winter 2019, Winter 2023, Winter 2024.
  • Enrolment Statistics (Winter 2017, recent)
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