Previous |  Up |  Next

Article

Keywords:
doubly nonlinear parabolic equation; generalized solution; bounded solution; maximum modulus; a priori estimate
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.
References:
[1] Lions J.L.: Quelques methods de resolution des problèmes aux limites non linéaires. Dunod. Gauthier-Villars, Paris, 1969. MR 0259693
[2] Alt H.W., Luckhaus S.: Quasilinear elliptic-parabolic differential equations. Math. Z. 183 (1983), 311-341. MR 0706391 | Zbl 0497.35049
[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
[4] Liang Xiting, Liang Xuexin: Boundedness properties of solutions doubly nonlinear parabolic equations. Acta Math. Sci., English ed. 1994, supplement, pp.110-117.
[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
[6] Ladyzenskaja O.A., Ural'ceva N.N.: Linear and quasilinear elliptic equations. Academic Press. Beijing, 1987 (Chinese version). MR 0244627
[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
[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.
[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.
[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.
Partner of
EuDML logo