Porous Medium Type Equations with a Quadratic Gradient Term

Daniela Giachetti; Giulia Maroscia

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 753-759
  • ISSN: 0392-4041

Abstract

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We show an existence result for the Cauchy-Dirichlet problem in Q T = Ω × ( 0 , T ) for parabolic equations with degenerate principal part (of porous medium type) with a lower order term having a quadratic growth with respect to the gradient. The right hand side of the equation f and the initial datum u 0 are bounded nonnegative functions.

How to cite

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Giachetti, Daniela, and Maroscia, Giulia. "Porous Medium Type Equations with a Quadratic Gradient Term." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 753-759. <http://eudml.org/doc/290394>.

@article{Giachetti2007,
abstract = {We show an existence result for the Cauchy-Dirichlet problem in $Q_T = \Omega \times (0, T)$ for parabolic equations with degenerate principal part (of porous medium type) with a lower order term having a quadratic growth with respect to the gradient. The right hand side of the equation $f$ and the initial datum $u_0$ are bounded nonnegative functions.},
author = {Giachetti, Daniela, Maroscia, Giulia},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {753-759},
publisher = {Unione Matematica Italiana},
title = {Porous Medium Type Equations with a Quadratic Gradient Term},
url = {http://eudml.org/doc/290394},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Giachetti, Daniela
AU - Maroscia, Giulia
TI - Porous Medium Type Equations with a Quadratic Gradient Term
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 753
EP - 759
AB - We show an existence result for the Cauchy-Dirichlet problem in $Q_T = \Omega \times (0, T)$ for parabolic equations with degenerate principal part (of porous medium type) with a lower order term having a quadratic growth with respect to the gradient. The right hand side of the equation $f$ and the initial datum $u_0$ are bounded nonnegative functions.
LA - eng
UR - http://eudml.org/doc/290394
ER -

References

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  2. BOCCARDO, L. - MURAT, F. - PUEL, J. P., Existence results for some quasilinear parabolic equations, Nonlinear Anal. T.M.A., 13, 4 (1989), 373-392. Zbl0705.35066MR987375DOI10.1016/0362-546X(89)90045-X
  3. DALL'AGLIO, A. - GIACHETTI, D. - LEONE, C. - SEGURA DE LEON, S., Quasi-linear Parabolic Equations With Degenerate Coercivity having a Quadratic Gradient Term, Ann. Inst. H. Poincaré Anal. Non Linéaire, 23, 1 (2006), 97-126. Zbl1103.35040MR2194583DOI10.1016/j.anihpc.2005.02.006
  4. DI BENEDETTO, E. - URBANO, J. M. - VESPRI, V., Current issues on singular and degenerate evolution equations, in Evolutionary Equations. Vol. I, Handb. Differ. Equ., 169-286, North-Holland, Amsterdam, The Netherlands (2004). Zbl1082.35002MR2103698
  5. GAGNEUX, G. - MADAUNE-TORT, M., Analyse mathématique de modèles non linéaires de l'ingénierie pétrolière, Mathématiqes and Applications, 22, SMAI (1996). Zbl0842.35126MR1616513
  6. LIONS, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthier-Villars, Paris (1969). Zbl0189.40603MR259693
  7. MAROSCIA, G., Boundary value problems for quasilinear degenerate equations modeling fluid flows in porous media, Ph. D. Thesis, Università di Roma ``La Sapienza'' (2006). 
  8. PORZIO, M. M. - VESPRI, V., Holder Estimates for Local Solutions of Some Doubly Nonlinear Degenerate Parabolic Equations, J. Differential Equations, 103, 1 (1993), 146-178. Zbl0796.35089MR1218742DOI10.1006/jdeq.1993.1045
  9. VAZQUEZ, J. L., The Porous Medium Equation. Mathematical Theory, Oxford Univ. Press (2006). Zbl1124.35035MR2286292

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