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Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates
1. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain |
2. | School of Mathematics, Watson Building, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom |
3. | Laboratoire de Mathématiques de Versailles, CNRS UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines, 45 Avenue de États-Unis, 78035 Versailles cedex, France |
References:
[1] |
M. J. Cáceres, J. A. Cañizo and S. Mischler, Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations,, J. Math. Pures Appl. (9), 96 (2011), 334.
doi: 10.1016/j.matpur.2011.01.003. |
[2] |
M. Doumic Jauffret and P. Gabriel, Eigenelements of a general aggregation-fragmentation model,, Math. Models Methods Appl. Sci., 20 (2010), 757.
doi: 10.1142/S021820251000443X. |
[3] |
M. Escobedo, S. Mischler and M. Rodríguez Ricard, On self-similarity and stationary problem for fragmentation and coagulation models,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 99.
doi: 10.1016/j.anihpc.2004.06.001. |
[4] |
P. Gabriel, "Équations de Transport-Fragmentation et Applications aux Maladies à Prions [Transport-Fragmentation Equations and Applications to Prion Diseases],", Ph.D thesis, (2011). Google Scholar |
[5] |
P. Laurençot and B. Perthame, Exponential decay for the growth-fragmentation/cell-division equation,, Comm. Math. Sci., 7 (2009), 503.
|
[6] |
J. A. J. Metz and O. Diekmann, eds., "The Dynamics of Physiologically Structured Populations,", Lecture notes in Biomathematics, 68 (1986).
|
[7] |
P. Michel, Existence of a solution to the cell division eigenproblem,, Math. Models Methods Appl. Sci., 16 (2006), 1125.
doi: 10.1142/S0218202506001480. |
[8] |
P. Michel, S. Mischler and B. Perthame, General entropy equations for structured population models and scattering,, C. R. Math. Acad. Sci. Paris, 338 (2004), 697.
doi: 10.1016/j.crma.2004.03.006. |
[9] |
P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: An illustration on growth models,, J. Math. Pures Appl. (9), 84 (2005), 1235.
doi: 10.1016/j.matpur.2005.04.001. |
[10] |
B. Perthame, "Transport Equations in Biology,", Frontiers in Mathematics, (2007).
|
[11] |
B. Perthame and L. Ryzhik, Exponential decay for the fragmentation or cell-division equation,, J. Differential Equations, 210 (2005), 155.
doi: 10.1016/j.jde.2004.10.018. |
[12] |
B. Perthame and D. Salort, Distributed elapsed time model for neuron networks,, in preparation., (). Google Scholar |
[13] |
R. Wong, "Asymptotic Approximation of Integrals,", Corrected reprint of the 1989 original, 34 (1989).
doi: 10.1137/1.9780898719260. |
show all references
References:
[1] |
M. J. Cáceres, J. A. Cañizo and S. Mischler, Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations,, J. Math. Pures Appl. (9), 96 (2011), 334.
doi: 10.1016/j.matpur.2011.01.003. |
[2] |
M. Doumic Jauffret and P. Gabriel, Eigenelements of a general aggregation-fragmentation model,, Math. Models Methods Appl. Sci., 20 (2010), 757.
doi: 10.1142/S021820251000443X. |
[3] |
M. Escobedo, S. Mischler and M. Rodríguez Ricard, On self-similarity and stationary problem for fragmentation and coagulation models,, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), 99.
doi: 10.1016/j.anihpc.2004.06.001. |
[4] |
P. Gabriel, "Équations de Transport-Fragmentation et Applications aux Maladies à Prions [Transport-Fragmentation Equations and Applications to Prion Diseases],", Ph.D thesis, (2011). Google Scholar |
[5] |
P. Laurençot and B. Perthame, Exponential decay for the growth-fragmentation/cell-division equation,, Comm. Math. Sci., 7 (2009), 503.
|
[6] |
J. A. J. Metz and O. Diekmann, eds., "The Dynamics of Physiologically Structured Populations,", Lecture notes in Biomathematics, 68 (1986).
|
[7] |
P. Michel, Existence of a solution to the cell division eigenproblem,, Math. Models Methods Appl. Sci., 16 (2006), 1125.
doi: 10.1142/S0218202506001480. |
[8] |
P. Michel, S. Mischler and B. Perthame, General entropy equations for structured population models and scattering,, C. R. Math. Acad. Sci. Paris, 338 (2004), 697.
doi: 10.1016/j.crma.2004.03.006. |
[9] |
P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: An illustration on growth models,, J. Math. Pures Appl. (9), 84 (2005), 1235.
doi: 10.1016/j.matpur.2005.04.001. |
[10] |
B. Perthame, "Transport Equations in Biology,", Frontiers in Mathematics, (2007).
|
[11] |
B. Perthame and L. Ryzhik, Exponential decay for the fragmentation or cell-division equation,, J. Differential Equations, 210 (2005), 155.
doi: 10.1016/j.jde.2004.10.018. |
[12] |
B. Perthame and D. Salort, Distributed elapsed time model for neuron networks,, in preparation., (). Google Scholar |
[13] |
R. Wong, "Asymptotic Approximation of Integrals,", Corrected reprint of the 1989 original, 34 (1989).
doi: 10.1137/1.9780898719260. |
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