Ecuaţii cu derivate partiale (2) |
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Cadre didactice indrumatoare |
Prof. Dr. PRECUP Radu, r.precup@math.ubbcluj.ro Prof. Dr. TRIF Damian, dtrif@math.ubbcluj.ro Conf. Dr. BEGE Antal, bege@math.ubbcluj.ro |
Obiective |
Perfectionarea instrumentelor de lucru in spatii Sobolev.
Pregatirea trecerii la studiul problemelor la limita neliniare. |
Continut |
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. 10. Probleme eliptice semilineare. |
Bibliografie |
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., Ecuatii cu derivate partiale, 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. Enc., Bucuresti, 1981 (Bevezetés a parciális differenciálegyenletek elméletébe, Muszaki Kiadó, Budapest, 1980). 10. Trif, D., Ecuatii cu derivate partiale, UBB, Cluj, 1993. |
Evaluare |
Examen. |