The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations

Xi Ting Liang; Wu Zaide

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 109-119
  • ISSN: 0010-2628

Abstract

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The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.

How to cite

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Liang, Xi Ting, and Zaide, Wu. "The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 109-119. <http://eudml.org/doc/248099>.

@article{Liang1997,
abstract = {The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.},
author = {Liang, Xi Ting, Zaide, Wu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {doubly nonlinear parabolic equation; generalized solution; bounded solution; maximum modulus; a priori estimate; generalized solution; bounded solution},
language = {eng},
number = {1},
pages = {109-119},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations},
url = {http://eudml.org/doc/248099},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Liang, Xi Ting
AU - Zaide, Wu
TI - The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 109
EP - 119
AB - The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.
LA - eng
KW - doubly nonlinear parabolic equation; generalized solution; bounded solution; maximum modulus; a priori estimate; generalized solution; bounded solution
UR - http://eudml.org/doc/248099
ER -

References

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  1. Lions J.L., Quelques methods de resolution des problèmes aux limites non linéaires, Dunod. Gauthier-Villars, Paris, 1969. MR0259693
  2. Alt H.W., Luckhaus S., Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341. (1983) Zbl0497.35049MR0706391
  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. (1988) MR0957665
  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. MR0241822
  6. Ladyzenskaja O.A., Ural'ceva N.N., Linear and quasilinear elliptic equations, Academic Press. Beijing, 1987 (Chinese version). MR0244627
  7. Miranda C., Alcune osservazioni sulla maggiorazione in L ν delle soluzioni deboli delle equazioni ellittiche del secondo ordine, Ann. Mat. Pura Appl. 61 (1963), 151-169. (1963) MR0177187
  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. (1988) 
  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. (1989) 
  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. (1989) 

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