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On eigenelements sensitivity for compact self-adjoint operators and applications
A geological delayed response model for stratigraphic reconstructions
1. | LaSIE, UMR-CNRS 7356, Université de La Rochelle, Avenue Michel Crépeau, 17000 La Rochelle, France, France |
References:
[1] |
L. Ambrosio, C. De Lellis and J. Maly, On the chain rule for the divergence of BV-like vector fields: Applications, partial results, open problems, Contemporary Mathematics, 446 (2007), 31-67.
doi: 10.1090/conm/446/08625. |
[2] |
S. N. Antontsev, G. Gagneux, R. Luce and G. Vallet, A non-standard free boundary problem arising from stratigraphy, Analysis and Applications, 4 (2006), 209-236.
doi: 10.1142/S0219530506000759. |
[3] |
S. N. Antontsev, G. Gagneux, R. Luce and G. Vallet, New unilateral problems in stratigraphy, ESAIM: Mathematical Modelling and Numerical Analysis, 40 (2006), 765-784.
doi: 10.1051/m2an:2006029. |
[4] |
S. N. Antontsev, G. Gagneux, A. Mokrani and G. Vallet, Stratigraphic modelling by the way of a pseudoparabolic problem with constraint, Advances in Mathematical Sciences and Applications, 19 (2009), 195-209. |
[5] |
S. N. Antontsev, G. Gagneux and G. Vallet, On some stratigraphic control problems, Prikladnaya Mekhanika Tekhnicheskaja Fisika, 44 (2003), 85-94 (in Russian). English version: Journal of Applied Mechanics and Technical Physics, 44 (2003), 821-828.
doi: 10.1023/A:1026287705015. |
[6] |
V. R. Baker and D. F. Ritter, Competence of rivers to transport coarse bedload material, Geological Society of America Bulletin, 86 (1975), 975-978. |
[7] |
G. I. Barenblatt, M. Bertsch, R. D. Passo and M. Ughi, A degenerate pseudoparabolic regularization of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow, SIAM Journal on Mathematical Analysis, 24 (1993), 1414-1439.
doi: 10.1137/0524082. |
[8] |
J. Blum, G. Dobranszky, R. Eymard and R. Masson, Identification of a stratigraphic model with seismic constraints, Inverse problems, 22 (2006), 1207-1225.
doi: 10.1088/0266-5611/22/4/006. |
[9] |
A. Cimetière, F. Delvare and F. Pons, Une méthode inverse d'ordre un pour les problèmes de complétion de données, Comptes rendus mécanique, 333 (2005), 123-126. |
[10] |
A. Cimetiere, F. Delvare, M. Jaoua and F. Pons, An inversion method for harmonic functions reconstruction, International journal of thermal sciences, 41 (2002), 509-516. |
[11] |
A. Cimetiere, F. Delvare, M. Jaoua and F. Pons, Solution of the Cauchy problem using iterated Tikhonov regularization, Inverse Problems, 17 (2001), 553-570.
doi: 10.1088/0266-5611/17/3/313. |
[12] |
S. Clain, Elliptic operators of divergence type with Hölder coefficients in fractional Sobolev spaces, Rend. Mat. Appl, 17 (1997), 207-236. |
[13] |
I. Csato, D. Granjeon, O. Catuneanu and G. R. Baum, A three-dimensional stratigraphic model for the Messinian crisis in the Pannonian Basin, eastern Hungary, Basin Research, 25 (2013), 121-148. |
[14] |
J. I. Díaz and S. Shmarev, Lagrangian approach to the study of level sets: Application to a free boundary problem in climatology, Archive for Rational Mechanics and Analysis, 194 (2009), 75-103.
doi: 10.1007/s00205-008-0164-y. |
[15] |
G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique, Travaux et Recherches Mathématiques, Dunod, Paris, 1972. |
[16] |
L. C. Evans and M. Portilheiro, Irreversibility and hysteresis for a forward-backward diffusion equation, Math. Models Methods Appl. Sci., 14 (2004), 1599-1620.
doi: 10.1142/S0218202504003763. |
[17] |
L. C. Evans, A survey of entropy methods for partial differential equations, Bull. Amer. Math. Soc. (N.S.), 41 (2004), 409-438.
doi: 10.1090/S0273-0979-04-01032-8. |
[18] |
R. Eymard, T. Gallouët, D. Granjeon, R. Masson and Q. H. Tran, Multi-lithology stratigraphic model under maximum erosion rate constraint, International Journal for Numerical Methods in Engineering, 60 (2004), 527-548.
doi: 10.1002/nme.974. |
[19] |
R. Eymard, T. Gallouët, V. Gervais and R. Masson, Convergence of a numerical scheme for stratigraphic modeling, SIAM Journal on Numerical Analysis, 43 (2005), 474-501.
doi: 10.1137/S0036142903426208. |
[20] |
R. Eymard and T. Gallouët, Analytical and numerical study of a model of erosion and sedimentation, SIAM Journal on Numerical Analysis, 43 (2006), 2344-2370.
doi: 10.1137/040605874. |
[21] |
R. Eymard and T. Gallouët, A partial differential inequality in geological models, Chinese Annals of Mathematics, Series B, 28 (2007), 709-736.
doi: 10.1007/s11401-006-0215-3. |
[22] |
G. Gagneux and M. Madaune-Tort, Analyse Mathématique de Modèles non Linéaires de L'ingénierie Pétrolière (Vol. 22), Springer, 1995. |
[23] |
G. Gagneux and G. Vallet, Sur des problèmes d'asservissements stratigraphiques. A tribute to J.-L. Lions, ESAIM: Control, Optimisation and Calculus of Variations, 8 (2002), 715-739.
doi: 10.1051/cocv:2002055. |
[24] |
G. Gagneux, R. Masson, A. Plouvier-Debaigt, G. Vallet and S. Wolf, Vertical compaction in a faulted sedimentary basin, ESAIM: Mathematical Modelling and Numerical Analysis, 37 (2003), 373-388.
doi: 10.1051/m2an:2003032. |
[25] |
V. Gervais and R. Masson, Mathematical and numerical analysis of a stratigraphic model, ESAIM: Mathematical Modelling and Numerical Analysis, 38 (2004), 585-611.
doi: 10.1051/m2an:2004035. |
[26] |
D. Granjeon, Q. Huy Tran, R. Masson and R. Glowinski, Modèle Stratigraphique Multilithologique Sous Contrainte de Taux D'érosion Maximum, Institut Français du Pétrole. Internal report, 2000. |
[27] |
Z. Gvirtzman, I. Csato and D. Granjeon, Constraining sediment transport to deep marine basins through submarine channels: The Levant margin in the Late Cenozoic, Marine Geology, 347 (2014), 12-26. |
[28] |
N. Hawie, R. Deschamps, F. H. Nader, C. Gorini, C. Müller, D. Desmares ... and F. Baudin, Sedimentological and stratigraphic evolution of northern Lebanon since the Late Cretaceous: implications for the Levant margin and basin, Arabian Journal of Geosciences, (2013), 1-27. |
[29] |
E. Leroux, M. Rabineau, D. Aslanian, D. Granjeon, L. Droz and C. Gorini, Stratigraphic simulations of the shelf of the Gulf of Lions: testing subsidence rates and sea-level curves during the Pliocene and Quaternary, Terra Nova, 2014. |
[30] |
J. L. Lions, Contrôle Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles (Vol. 1), Paris: Dunod, 1968. |
[31] |
J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (Vol. 31), Paris: Dunod, 1969. |
[32] |
Y. Mualem and G. Dagan, A dependent domain model of capillary hysteresis, Water Resources Research, 11 (1975), 452-460. |
[33] |
J. Nečas and S. Mas-Gallic, Écoulements de Fluide: Compacitè par Entropie (Vol. 10), Masson, 1989. |
[34] |
A. Poulovassilis and E. C. Childs, The hysteresis of pore water: the non-independence of domains, Soil Science, 112 (1971), 301-312. |
[35] |
J. C. Rivenaes, Application of a dual-lithology, depth-dependent diffusion equation in stratigraphic simulation, Basin Research, 4 (1992), 133-146. |
[36] |
S. Shmarev and G. Vallet, Local in time solvability of a nonstandard free boundary problem in stratigraphy: A Lagrangian approach, Nonlinear Analysis: Real World Applications, 22 (2015), 404-422.
doi: 10.1016/j.nonrwa.2014.10.001. |
[37] |
R. Tolosana-Delgado and H. von Eynatten, Grain-size control on petrographic composition of sediments: Compositional regression and rounded zeros, Mathematical Geosciences, 41 (2009), 869-886. |
[38] |
G. Vallet, Sur une loi de conservation issue de la géologie, Comptes Rendus Mathématiques, 337 (2003), 559-564.
doi: 10.1016/j.crma.2003.08.012. |
show all references
References:
[1] |
L. Ambrosio, C. De Lellis and J. Maly, On the chain rule for the divergence of BV-like vector fields: Applications, partial results, open problems, Contemporary Mathematics, 446 (2007), 31-67.
doi: 10.1090/conm/446/08625. |
[2] |
S. N. Antontsev, G. Gagneux, R. Luce and G. Vallet, A non-standard free boundary problem arising from stratigraphy, Analysis and Applications, 4 (2006), 209-236.
doi: 10.1142/S0219530506000759. |
[3] |
S. N. Antontsev, G. Gagneux, R. Luce and G. Vallet, New unilateral problems in stratigraphy, ESAIM: Mathematical Modelling and Numerical Analysis, 40 (2006), 765-784.
doi: 10.1051/m2an:2006029. |
[4] |
S. N. Antontsev, G. Gagneux, A. Mokrani and G. Vallet, Stratigraphic modelling by the way of a pseudoparabolic problem with constraint, Advances in Mathematical Sciences and Applications, 19 (2009), 195-209. |
[5] |
S. N. Antontsev, G. Gagneux and G. Vallet, On some stratigraphic control problems, Prikladnaya Mekhanika Tekhnicheskaja Fisika, 44 (2003), 85-94 (in Russian). English version: Journal of Applied Mechanics and Technical Physics, 44 (2003), 821-828.
doi: 10.1023/A:1026287705015. |
[6] |
V. R. Baker and D. F. Ritter, Competence of rivers to transport coarse bedload material, Geological Society of America Bulletin, 86 (1975), 975-978. |
[7] |
G. I. Barenblatt, M. Bertsch, R. D. Passo and M. Ughi, A degenerate pseudoparabolic regularization of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow, SIAM Journal on Mathematical Analysis, 24 (1993), 1414-1439.
doi: 10.1137/0524082. |
[8] |
J. Blum, G. Dobranszky, R. Eymard and R. Masson, Identification of a stratigraphic model with seismic constraints, Inverse problems, 22 (2006), 1207-1225.
doi: 10.1088/0266-5611/22/4/006. |
[9] |
A. Cimetière, F. Delvare and F. Pons, Une méthode inverse d'ordre un pour les problèmes de complétion de données, Comptes rendus mécanique, 333 (2005), 123-126. |
[10] |
A. Cimetiere, F. Delvare, M. Jaoua and F. Pons, An inversion method for harmonic functions reconstruction, International journal of thermal sciences, 41 (2002), 509-516. |
[11] |
A. Cimetiere, F. Delvare, M. Jaoua and F. Pons, Solution of the Cauchy problem using iterated Tikhonov regularization, Inverse Problems, 17 (2001), 553-570.
doi: 10.1088/0266-5611/17/3/313. |
[12] |
S. Clain, Elliptic operators of divergence type with Hölder coefficients in fractional Sobolev spaces, Rend. Mat. Appl, 17 (1997), 207-236. |
[13] |
I. Csato, D. Granjeon, O. Catuneanu and G. R. Baum, A three-dimensional stratigraphic model for the Messinian crisis in the Pannonian Basin, eastern Hungary, Basin Research, 25 (2013), 121-148. |
[14] |
J. I. Díaz and S. Shmarev, Lagrangian approach to the study of level sets: Application to a free boundary problem in climatology, Archive for Rational Mechanics and Analysis, 194 (2009), 75-103.
doi: 10.1007/s00205-008-0164-y. |
[15] |
G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique, Travaux et Recherches Mathématiques, Dunod, Paris, 1972. |
[16] |
L. C. Evans and M. Portilheiro, Irreversibility and hysteresis for a forward-backward diffusion equation, Math. Models Methods Appl. Sci., 14 (2004), 1599-1620.
doi: 10.1142/S0218202504003763. |
[17] |
L. C. Evans, A survey of entropy methods for partial differential equations, Bull. Amer. Math. Soc. (N.S.), 41 (2004), 409-438.
doi: 10.1090/S0273-0979-04-01032-8. |
[18] |
R. Eymard, T. Gallouët, D. Granjeon, R. Masson and Q. H. Tran, Multi-lithology stratigraphic model under maximum erosion rate constraint, International Journal for Numerical Methods in Engineering, 60 (2004), 527-548.
doi: 10.1002/nme.974. |
[19] |
R. Eymard, T. Gallouët, V. Gervais and R. Masson, Convergence of a numerical scheme for stratigraphic modeling, SIAM Journal on Numerical Analysis, 43 (2005), 474-501.
doi: 10.1137/S0036142903426208. |
[20] |
R. Eymard and T. Gallouët, Analytical and numerical study of a model of erosion and sedimentation, SIAM Journal on Numerical Analysis, 43 (2006), 2344-2370.
doi: 10.1137/040605874. |
[21] |
R. Eymard and T. Gallouët, A partial differential inequality in geological models, Chinese Annals of Mathematics, Series B, 28 (2007), 709-736.
doi: 10.1007/s11401-006-0215-3. |
[22] |
G. Gagneux and M. Madaune-Tort, Analyse Mathématique de Modèles non Linéaires de L'ingénierie Pétrolière (Vol. 22), Springer, 1995. |
[23] |
G. Gagneux and G. Vallet, Sur des problèmes d'asservissements stratigraphiques. A tribute to J.-L. Lions, ESAIM: Control, Optimisation and Calculus of Variations, 8 (2002), 715-739.
doi: 10.1051/cocv:2002055. |
[24] |
G. Gagneux, R. Masson, A. Plouvier-Debaigt, G. Vallet and S. Wolf, Vertical compaction in a faulted sedimentary basin, ESAIM: Mathematical Modelling and Numerical Analysis, 37 (2003), 373-388.
doi: 10.1051/m2an:2003032. |
[25] |
V. Gervais and R. Masson, Mathematical and numerical analysis of a stratigraphic model, ESAIM: Mathematical Modelling and Numerical Analysis, 38 (2004), 585-611.
doi: 10.1051/m2an:2004035. |
[26] |
D. Granjeon, Q. Huy Tran, R. Masson and R. Glowinski, Modèle Stratigraphique Multilithologique Sous Contrainte de Taux D'érosion Maximum, Institut Français du Pétrole. Internal report, 2000. |
[27] |
Z. Gvirtzman, I. Csato and D. Granjeon, Constraining sediment transport to deep marine basins through submarine channels: The Levant margin in the Late Cenozoic, Marine Geology, 347 (2014), 12-26. |
[28] |
N. Hawie, R. Deschamps, F. H. Nader, C. Gorini, C. Müller, D. Desmares ... and F. Baudin, Sedimentological and stratigraphic evolution of northern Lebanon since the Late Cretaceous: implications for the Levant margin and basin, Arabian Journal of Geosciences, (2013), 1-27. |
[29] |
E. Leroux, M. Rabineau, D. Aslanian, D. Granjeon, L. Droz and C. Gorini, Stratigraphic simulations of the shelf of the Gulf of Lions: testing subsidence rates and sea-level curves during the Pliocene and Quaternary, Terra Nova, 2014. |
[30] |
J. L. Lions, Contrôle Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles (Vol. 1), Paris: Dunod, 1968. |
[31] |
J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (Vol. 31), Paris: Dunod, 1969. |
[32] |
Y. Mualem and G. Dagan, A dependent domain model of capillary hysteresis, Water Resources Research, 11 (1975), 452-460. |
[33] |
J. Nečas and S. Mas-Gallic, Écoulements de Fluide: Compacitè par Entropie (Vol. 10), Masson, 1989. |
[34] |
A. Poulovassilis and E. C. Childs, The hysteresis of pore water: the non-independence of domains, Soil Science, 112 (1971), 301-312. |
[35] |
J. C. Rivenaes, Application of a dual-lithology, depth-dependent diffusion equation in stratigraphic simulation, Basin Research, 4 (1992), 133-146. |
[36] |
S. Shmarev and G. Vallet, Local in time solvability of a nonstandard free boundary problem in stratigraphy: A Lagrangian approach, Nonlinear Analysis: Real World Applications, 22 (2015), 404-422.
doi: 10.1016/j.nonrwa.2014.10.001. |
[37] |
R. Tolosana-Delgado and H. von Eynatten, Grain-size control on petrographic composition of sediments: Compositional regression and rounded zeros, Mathematical Geosciences, 41 (2009), 869-886. |
[38] |
G. Vallet, Sur une loi de conservation issue de la géologie, Comptes Rendus Mathématiques, 337 (2003), 559-564.
doi: 10.1016/j.crma.2003.08.012. |
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