"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Partial differential equations (2)
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
ME004
6
2+1+0
5
compulsory
Matematică
ME004
8
2+2+0
6
optional
Matematici aplicate
Teaching Staff in Charge
Prof. TRIF Damian, Ph.D.,  dtrifmath.ubbcluj.ro
Prof. PRECUP Radu, Ph.D.,  r.precupmath.ubbcluj.ro
Assoc.Prof. BEGE Antal, Ph.D.,  begemath.ubbcluj.ro
Aims
Improvement of the working methods in Sobolev spaces in view of
the study of nonlinear boundary value problems.
Content
Distributions; Sobolev spaces; Fourier transform; Generalized solutions
to elliptic problems; Regularity results. Maximum principles.
Eigenvalues and eigenfunctions. Semilinear elliptic problems.
References
1. ADAMS, R.A., Sobolev spaces, Academic Press, 1975.
2. BARBU, V., Probleme la limita pentru ecuatii cu derivate partiale, Ed. Acad. Române, Bucuresti, 1993.
3. DEBNAT, L., Non-linear partial differential equations for scientists and engineers, Birkhauser, Berlin, 1997.
4. GILBARG, D., TRUDINGER, N.S., Elliptic partial differential equations of second order, Springer, Berlin, 1983.
5. O'REGAN, D., PRECUP, R., Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001.
6. PRECUP, R., Lectii de ecuatii cu derivate partiale, Presa Universitara Clujeana, 2004.
7. RAUCH, J., Partial differential equations, Springer, Berlin, 1991.
8. SZILAGYI P., Másodrendu parciális differenciálegyenletek, BBTE, Kolozsvár, 1998.
9. VLADIMIROV, V.S., Ecuatiile fizicii matematice, Ed. St. Enc., Bucuresti, 1981 (Bevezetés a parciális differenciálegyenletek elméletébe, Muszaki Kiadó, Budapest, 1980).
10. TRIF, D., Ecuatii cu derivate partiale, UBB, Cluj, 1993.


Assessment
Midterm exam 30%
Final written exam 70%.