New unilateral problems in stratigraphy

Stanislav N. Antontsev; Gérard Gagneux; Robert Luce; Guy Vallet

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 4, page 765-784
  • ISSN: 0764-583X

Abstract

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This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type 0 t u - d i v { H ( t u + E ) u } , where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation law, with a unilateral constraint on the outflow boundary. Then, we give a study of the 1-D case with numerical illustrations.

How to cite

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Antontsev, Stanislav N., et al. "New unilateral problems in stratigraphy." ESAIM: Mathematical Modelling and Numerical Analysis 40.4 (2006): 765-784. <http://eudml.org/doc/249709>.

@article{Antontsev2006,
abstract = { This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type $0\in \partial _\{t\}u-div\\{H(\partial _\{t\}u+E)\nabla u\\}$, where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation law, with a unilateral constraint on the outflow boundary. Then, we give a study of the 1-D case with numerical illustrations. },
author = {Antontsev, Stanislav N., Gagneux, Gérard, Luce, Robert, Vallet, Guy},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Stratigraphic models; weather limited; degenerated parabolic-hyperbolic conservation laws.; stratigraphic models; degenerated parabolic-hyperbolic conservation laws},
language = {eng},
month = {11},
number = {4},
pages = {765-784},
publisher = {EDP Sciences},
title = {New unilateral problems in stratigraphy},
url = {http://eudml.org/doc/249709},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Antontsev, Stanislav N.
AU - Gagneux, Gérard
AU - Luce, Robert
AU - Vallet, Guy
TI - New unilateral problems in stratigraphy
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/11//
PB - EDP Sciences
VL - 40
IS - 4
SP - 765
EP - 784
AB - This work deals with the study of some stratigraphic models for the formation of geological basins under a maximal erosion rate constrain. It leads to introduce differential inclusions of degenerated hyperbolic-parabolic type $0\in \partial _{t}u-div\{H(\partial _{t}u+E)\nabla u\}$, where H is the maximal monotonous graph of the Heaviside function and E is a given non-negative function. Firstly, we present the new and realistic models and an original mathematical formulation, taking into account the weather-limited rate constraint in the conservation law, with a unilateral constraint on the outflow boundary. Then, we give a study of the 1-D case with numerical illustrations.
LA - eng
KW - Stratigraphic models; weather limited; degenerated parabolic-hyperbolic conservation laws.; stratigraphic models; degenerated parabolic-hyperbolic conservation laws
UR - http://eudml.org/doc/249709
ER -

References

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  1. S.N. Antontsev, D. Etienne, G. Gagneux and G. Vallet, New unilateral problems in stratigraphy. Publication interne du Laboratoire de Mathématiques Appliquées, UMR-CNRS 5142, Université de Pau, No. 05/13 (2005).  Zbl1133.35388
  2. S.N. Antontsev, G. Gagneux, R. Luce and G. Vallet, Weather limited constraint in stratigraphy. International conference “Tikhonov and Contemporary Mathematics": section 5, Mathematical Geophysics, Moscow (2006) 7–8.  
  3. S.N. Antontsev, G. Gagneux and G. Vallet, Analyse mathématique d'un modèle d'asservissement stratigraphique. Approche gravitationnelle d'un processus de sédimentation sous contrainte d'érosion maximale. Publication interne du Laboratoire de Mathématiques Appliquées, UMR-CNRS 5142, Université de Pau, No. 01/23 (2001).  
  4. S.N. Antontsev, G. Gagneux and G. Vallet, On some stratigraphic control problems, Prikladnaya Mekhanika Tekhnicheskaja Fisika (Novosibirsk)44 (2003) 85–94 (in Russian), and Journal of Applied Mechanics and Technical Physics (New York)44 (2003) 821–828.  Zbl1038.76039
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  7. D. Etienne, Contribution à l'analyse mathématique de modèles stratigraphiques. Thèse de l'Université de Pau, France (2004).  
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  10. G. Gagneux, R. Luce and G. Vallet, A non-standard free-boundary problem arising from stratigraphy. Publication interne du Laboratoire de Mathématiques Appliquées, UMR-CNRS 5142, Université de Pau, No. 04/33 (2004).  Zbl1096.35069
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  13. G. Gagneux and G. Vallet, A result of existence for an original convection-diffusion equation. Revista de la Real Academia de Ciencias, Serie A: Matemáticas (RACSAM)99 (2005) 125–131.  Zbl1090.35107
  14. T. Gallouët, Equations satisfaites par des limites de solutions approchées, conférence plénière, 34ème congrès d'analyse numérique, Anglet (Pyrénées Atlantiques), in Canum (2002) 87–96.  
  15. V. Gervais and R. Masson, Mathematical and numerical analysis of a stratigraphic model. ESAIM: M2AN38 (2004) 585-611.  Zbl1130.86315
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