Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term

A. Dall'Aglio; D. Giachetti; C. Leone; S. Segura de León

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 1, page 97-126
  • ISSN: 0294-1449

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Dall'Aglio, A., et al. "Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term." Annales de l'I.H.P. Analyse non linéaire 23.1 (2006): 97-126. <http://eudml.org/doc/78686>.

@article{DallAglio2006,
author = {Dall'Aglio, A., Giachetti, D., Leone, C., Segura de León, S.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {degenerate nonlinear parabolic problems; gradient term with quadratic growth; existence; regularity; bounded and unbounded solutions; distributional solutions; homogeneous Dirichlet boundary conditions},
language = {eng},
number = {1},
pages = {97-126},
publisher = {Elsevier},
title = {Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term},
url = {http://eudml.org/doc/78686},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Dall'Aglio, A.
AU - Giachetti, D.
AU - Leone, C.
AU - Segura de León, S.
TI - Quasi-linear parabolic equations with degenerate coercivity having a quadratic gradient term
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 1
SP - 97
EP - 126
LA - eng
KW - degenerate nonlinear parabolic problems; gradient term with quadratic growth; existence; regularity; bounded and unbounded solutions; distributional solutions; homogeneous Dirichlet boundary conditions
UR - http://eudml.org/doc/78686
ER -

References

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  1. [1] Alt H.W., Luckhaus S., Quasilinear elliptic-parabolic differential equations, Math. Z.183 (1983) 311-341. Zbl0497.35049MR706391
  2. [2] Andreu F., Mazón J.M., Segura de León S., Toledo J., Existence and uniqueness for a degenerate parabolic equation with L 1 data, Trans. Amer. Math. Soc.351 (1999) 285-306. Zbl0912.35092MR1433108
  3. [3] Aronson D.G., Serrin J., Local behavior of solutions of quasilinear parabolic equations, Arch. Rational Mech. Anal.25 (1967) 81-122. Zbl0154.12001MR244638
  4. [4] Aubin J.P., Un théorème de compacité, C. R. Acad. Sci.256 (1963) 5042-5044. Zbl0195.13002MR152860
  5. [5] Bénilan P., Boccardo L., Gallouët T., Gariepy R., Pierre M., Vázquez J.L., An L 1 theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Scuola Norm. Sup. Pisa22 (2) (1995) 240-273. Zbl0866.35037MR1354907
  6. [6] Blanchard D., Porretta A., Nonlinear parabolic equations with natural growth terms and measure initial data, Ann. Scuola Norm. Sup. Pisa Cl. Sci.30 (4) (2001) 583-622. Zbl1072.35089MR1896079
  7. [7] Boccardo L., Murat F., Puel J.P., Résultats d'existence pour certains problèmes elliptiques quasilinéaires, Ann. Scuola Norm. Sup. Pisa11 (1984) 213-235. Zbl0557.35051MR764943
  8. [8] Boccardo L., Murat F., Puel J.P., Existence results for some quasilinear parabolic equations, Nonlinear Anal.13 (1989) 373-392. Zbl0705.35066MR987375
  9. [9] Boccardo L., Porzio M.M., Bounded solutions for a class of quasi-linear parabolic problems with a quadratic gradient term, Progr. Nonlinear Differential Equations50 (2002) 39-48. Zbl1028.35058MR1944156
  10. [10] Boccardo L., Segura de León S., Trombetti C., Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic grandient term, J. Math. Pures Appl.80 (9) (2001) 919-940. Zbl1134.35358MR1865381
  11. [11] Brezis H., Analyse fonctionnelle. Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983. Zbl0511.46001MR697382
  12. [12] Dall'Aglio A., Giachetti D., Puel J.P., Nonlinear elliptic equations with natural growth in general domains, Ann. Mat. Pura Appl.181 (2002) 407-426. Zbl1097.35050MR1939689
  13. [13] A. Dall'Aglio, D. Giachetti, J.P. Puel, Nonlinear parabolic equations with natural growth in general domains, Bull. Un. Mat. Ital., in press. Zbl1117.35035
  14. [14] Dall'Aglio A., Orsina L., Nonlinear parabolic equations with natural growth conditions and L 1 data, Nonlinear Anal.27 (1996) 59-73. Zbl0861.35045MR1390712
  15. [15] DiBenedetto E., Degenerate Parabolic Equations, Springer-Verlag, New York, 1993. Zbl0794.35090MR1230384
  16. [16] Evans L.C., Partial Differential Equations, Graduate Stud. in Math., vol. 19, American Mathematical Society, Providence, RI, 1998. Zbl0902.35002
  17. [17] Ferone V., Murat F., Nonlinear problems having natural growth in the gradient: an existence result when the source terms are small, Nonlinear Anal.42 (2000) 1309-1326. Zbl1158.35358MR1780731
  18. [18] Ferone V., Posteraro M.R., Rakotoson J.M., L 1 -estimates for nonlinear elliptic problems withp-growth in the gradient, J. Ineq. Appl.3 (1999) 109-125. Zbl0928.35060MR1733106
  19. [19] Ferone V., Posteraro M.R., Rakotoson J.M., Nonlinear parabolic equations with p-growth and unbounded data, C. R. Acad. Sci. Paris Sèr. I Math.328 (1999) 291-296. Zbl0922.35075MR1675940
  20. [20] Ferone V., Posteraro M.R., Rakotoson J.M., Nonlinear parabolic problems with critical growth and unbounded data, Indiana Univ. Math. J.50 (3) (2001) 1201-1215. Zbl1256.35025MR1871353
  21. [21] Ladyzenskaja O.A., Solonnikov V.A., Ural'ceva N.N., Linear and Quasi-Linear Equations of Parabolic Type, Transl. Math. Monographs, vol. 23, Amer. Math. Soc., Providence, RI, 1968. Zbl0174.15403MR241821
  22. [22] Landes R., On the existence of weak solutions for quasilinear parabolic boundary value problems, Proc. Roy. Soc. Edinburgh Sect. A89 (1981) 217-237. Zbl0493.35054MR635759
  23. [23] Landes R., Mustonen V., On parabolic initial-boundary value problems with critical growth for the gradient, Ann. Inst. H. Poincaré Anal. Non Linéaire11 (1994) 135-158. Zbl0836.35078MR1267364
  24. [24] Mokrane A., Existence of bounded solutions of some nonlinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A107 (3–4) (1987) 313-326. Zbl0649.35044MR924524
  25. [25] Orsina L., Porzio M.M., L Q -estimate and existence of solutions for some nonlinear parabolic equations, Boll. Un. Math. Ital. B6 (1992) 631-647. Zbl0783.35026MR1191957
  26. [26] Porretta A., Regularity for entropy solutions of a class of parabolic equations with non regular initial datum, Dynamic Systems Appl.7 (1998) 53-71. Zbl0899.35049MR1612029
  27. [27] A. Porretta, S. Segura de León, Nonlinear elliptic equations having a gradient term with natural growth, Preprint. Zbl1158.35364
  28. [28] Prignet A., Existence and uniqueness of entropy solution of parabolic problems with L 1 data, Nonlinear Anal.28 (12) (1997) 1943-1954. Zbl0909.35075MR1436364
  29. [29] Simon J., Compact sets in the space L p ( 0 , T ; B ) , Ann. Mat. Pura Appl.146 (1987) 65-96. Zbl0629.46031MR916688

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