Ecuaţii cu derivate partiale (2) | Partial differential equations (2) |
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(Mathematics) |
Cadre didactice indrumatoare | Teaching Staff in Charge |
Prof. Dr. SZILAGYI Paul, szilagyp@cs.ubbcluj.ro Prof. Dr. TRIF Damian, dtrif@math.ubbcluj.ro |
Obiective | Aims |
Perfectionarea instrumentelor de lucru in spatii Sobolev. Pregatirea trecerii la studiul problemelor la limita neliniare. |
Improvement of the working methods in Sobolev spaces in view of the study of nonlinear boundary value problems. |
1. Complemente de teorie a distributiilor. Transformarea Fourier.
1. Spatii Sobolev. Operatorul de prelungire. 2. Teoremele de scufundare marginita ale lui Sobolev. 3. Inegalitatea lui Wirtinger-Poincare. 4. Teorema de scufundare compacta a lui Rellich-Kondrachov. 5. Dualul spatiilor Sobolev. 6. Teoria variationala a problemelor eliptice la limita. 7. Teoreme asupra regularitatii solutiei slabe. 8. Principiul de maxim pentru solutii slabe. 9. Valori si functii proprii pentru problema Dirichlet; prima valoare si functie proprie. |
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. Kalik, C., Ecuatii cu derivate partiale. Ed. St. si Enc. Bucuresti, 1980. 6. Precup, R., Ecuatii cu derivate partiale. Casa de Ed. Transilvania Press, Cluj, 1997. 7. Rauch, J., Partial differential equations. Springer, Berlin, 1991. 8. Szilágyi P., Másodrendu parciális differenciálegyenletek. BBTE, Kolozsvár 1998. 9. Vladimirov, V.S., Ecuatiile fizicii matematice. Ed. St si Enc. Bucuresti, 1981 (Bevezetés a parciális differenciálegyenletek elméletébe. Muszaki Kiadó, Budapest, 1980) 10. Trif, D., Ecuatii cu derivate partiale. UBB, Cluj, 1993 |
Evaluare | Assessment |
Examen. |
Exam. |