| Title:
|
The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations (English) |
| Author:
|
Liang, Xiting, |
| Author:
|
Zaide, Wu |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
109-119 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions. (English) |
| Keyword:
|
doubly nonlinear parabolic equation |
| Keyword:
|
generalized solution |
| Keyword:
|
bounded solution |
| Keyword:
|
maximum modulus |
| Keyword:
|
a priori estimate |
| MSC:
|
35B45 |
| MSC:
|
35K55 |
| MSC:
|
35K65 |
| idZBL:
|
Zbl 0887.35080 |
| idMR:
|
MR1455474 |
| . |
| Date available:
|
2009-01-08T18:29:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118906 |
| . |
| Reference:
|
[1] Lions J.L.: Quelques methods de resolution des problèmes aux limites non linéaires.Dunod. Gauthier-Villars, Paris, 1969. MR 0259693 |
| Reference:
|
[2] Alt H.W., Luckhaus S.: Quasilinear elliptic-parabolic differential equations.Math. Z. 183 (1983), 311-341. Zbl 0497.35049, MR 0706391 |
| Reference:
|
[3] Blanchard D., Francfort G.A.: Study of a doubly nonlinear heat equations with no growth assumptions on the parabolic term.SIAM J. Math. Anal. 19 (1988), 1032-1057. MR 0957665 |
| Reference:
|
[4] Liang Xiting, Liang Xuexin: Boundedness properties of solutions doubly nonlinear parabolic equations.Acta Math. Sci., English ed. 1994, supplement, pp.110-117. |
| Reference:
|
[5] Ladyzenskaja O.A., Solonnikov V.A., Ural'ceva N.N.: Linear and quasilinear equations of parabolic type.Transl. Math. Monographs # 23, AMS, Providence, Rhode Island, 1968. MR 0241822 |
| Reference:
|
[6] Ladyzenskaja O.A., Ural'ceva N.N.: Linear and quasilinear elliptic equations.Academic Press. Beijing, 1987 (Chinese version). MR 0244627 |
| Reference:
|
[7] Miranda C.: Alcune osservazioni sulla maggiorazione in $L^\nu $ delle soluzioni deboli delle equazioni ellittiche del secondo ordine.Ann. Mat. Pura Appl. 61 (1963), 151-169. MR 0177187 |
| Reference:
|
[8] Yu Minggi, Liang Xiting: A new estimate to the maximum of generalized solutions of quasilinear elliptic and parabolic equations (in Chinese).J. Shanxi Univ. (Nat. Sci. Ed.) 3 (1988), 7-12. |
| Reference:
|
[9] Lu Youwen, Liang Xiting: On a priori estimate of maximum modulus for generalized solutions of quasilinear elliptic equations (in Chinese).J. Tianjin Normal Univ. (Nat. Sci. Ed.) 1 (1989), 5-14. |
| Reference:
|
[10] Liang Xiting: An improvement to estimate of maximum modulus of generalized solutions of linear elliptic and parabolic equations of second order (in Chinese).Acta Sci. Nat. Univ. Sunyatseni 28.2 (1989), 78-80. |
| . |
