Nonlinear parabolic equations with natural growth terms and measure initial data

Dominique Blanchard; Alessio Porretta

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2001)

  • Volume: 30, Issue: 3-4, page 583-622
  • ISSN: 0391-173X

How to cite

top

Blanchard, Dominique, and Porretta, Alessio. "Nonlinear parabolic equations with natural growth terms and measure initial data." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 30.3-4 (2001): 583-622. <http://eudml.org/doc/84454>.

@article{Blanchard2001,
author = {Blanchard, Dominique, Porretta, Alessio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3-4},
pages = {583-622},
publisher = {Scuola normale superiore},
title = {Nonlinear parabolic equations with natural growth terms and measure initial data},
url = {http://eudml.org/doc/84454},
volume = {30},
year = {2001},
}

TY - JOUR
AU - Blanchard, Dominique
AU - Porretta, Alessio
TI - Nonlinear parabolic equations with natural growth terms and measure initial data
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2001
PB - Scuola normale superiore
VL - 30
IS - 3-4
SP - 583
EP - 622
LA - eng
UR - http://eudml.org/doc/84454
ER -

References

top
  1. [BBGGPV] P. Bénilan - L. Boccardo - T. Gallouët - R. Gariepy - M. Pierre - J.L. Vazquez, An L1-theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa Cl. Sci.22 (1995), 241-273. Zbl0866.35037MR1354907
  2. [B1] D. Blanchard, Truncations and monotonicity methods for parabolic equations, Nonlinear Anal.21 (1993), 725-743. Zbl0796.35077MR1246504
  3. [BlM] D. Blanchard - F. Murat, Renormalized solutions of nonlinear parabolic prob-[B1M] lems with L1 data : existence and uniqueness, Proc. Roy. Soc. Edinburgh Sect. A lems with L1 data: existance and uniqueness, Proc. Roy. Soc. Edinburgh Sect.A127 (1997), 1137-1152. Zbl0895.35050MR1489429
  4. [BlMR] D. Blanchard - F. Murat - H. Redwane, Existence et unicité de la solution renormalisée d'un problème parabolique non linéaire assez général, C.R. Acad. Sci. Paris, t. 329, Série 1 (1999), 575-580. Zbl0935.35073MR1717112
  5. [BR] D. Blanchard - H. Redwane, Renormalized solutions for a class of nonlinear evolution problems, J. Math. Pures Appl.77 (1998), 117-151. Zbl0907.35070MR1614645
  6. [BDGO] L. Boccardo - A. Dall'aglio - T. Gallouët - L. Orsina, Nonlinear parabolic equations with measure data, J. Funct. Anal.147 (1997), 237-258. Zbl0887.35082MR1453181
  7. [BDGM] L. Boccardo - I. Diaz - D. Giachetti - F. Murat, Existence of a solution for a weaker form of a nonlinear elliptic equation, Recent advances in nonlinear elliptic and parabolic problems (Nancy, 1988), Pitman Res. Notes Math. Ser.208, 229-246, Longman, 1989. Zbl0703.35063MR1035010
  8. [BG] L. Boccardo - T. Gallouët, Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal.87 (1989), 149-169. Zbl0707.35060MR1025884
  9. [BMP] L. Boccardo - F. Murat - J.P. Puel, Existence of bounded solutions for nonlinear elliptic unilateral problems, Ann. Mat. Pura Appl.152 (1988), 183-196. Zbl0687.35042MR980979
  10. [BMP2] L. Boccardo - F. Murat - J.P. Puel, Existence results for some quasilinear parabolic equations, Nonlinear Anal.13 (1989), 373-392. Zbl0705.35066MR987375
  11. [BF] H. Brézis - A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl.62 (1983), 73-97. Zbl0527.35043MR700049
  12. [CW] J. Carrillo - P. Wittbold, Uniqueness of renormalized solutions of degenerate elliptic-parabolic problems, J. Differential Equations156 (1999), 93-121. Zbl0932.35129MR1701806
  13. [DL] R.J. Di Perna - P.L. Lions, On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math.130 (1989), 321-366. Zbl0698.45010MR1014927
  14. [DMOP] G. Dal Maso - F. Murat - L. Orsina - A. Prignet, Renormalized solutions of elliptic equations with general measure data, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28 (1999), 741-808. Zbl0958.35045MR1760541
  15. [DO] A. Dall'aglio - L. Orsina, Nonlinear parabolic equations with natural growth conditions and L1 data, Nonlinear Anal.27 n. 1 (1996), 59-73. Zbl0861.35045MR1390712
  16. [GV] V.A. Galaktionov - J.L. Vazquez, Continuation of blowup solutions of nonlinear heat equations in several space dimensions, Comm. Pure Appl. Math.50 (1997), 1-67. Zbl0874.35057MR1423231
  17. [La] R. Landes, On the existence of weak solutions for quasilinear parabolic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A89 (1981), 217-237. Zbl0493.35054MR635759
  18. [LaMu] R. Landes - V. Mustonen, On parabolic initial-boundary value problems with critical growth for the gradient, Ann. Inst. H. Poincare Anal. Nonlinéaire, 11 (1994), 135-158. Zbl0836.35078MR1267364
  19. [L] J.L. Lions, "Quelques méthodes de résolution des problemes aux limites non lineaires", Dunod et Gauthiers-Villars, (1969). Zbl0189.40603MR259693
  20. [LM] P.L. Lions - F. Murat, Renormalized solutions for nonlinear elliptic equations, in preparation. 
  21. [P] A. Porretta, Existence results for nonlinear parabolic equations via strong convergence of truncations, Ann. Mat. Pura Appl. (4) 177 (1999), 143-172. Zbl0957.35066MR1747629
  22. [ST] S. Segura de Leon - J. Toledo, Regularity for entropy solutions of parabolic p-Laplacian type equations, Publ. Mat.43 (1999), 665-683. Zbl0962.35108MR1744624

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.