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Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation
Well-posedness for a model of individual clustering
1. | Institut de Mathématiques de Toulouse, Université de Toulouse, F-31062 Toulouse cedex 9 |
References:
[1] |
T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford Lecture Series in Mathematics and it Applications, 2006. |
[2] |
T. Cieślak, Ph. Laurençot and C. Morales-Rodrigo, Global existence and convergence to steady states in a chemorepulsion system, Parabolic and Navier-Stokes Equations, Part 1, 105-117, Banach Center Publ., 81, Part 1, Polish Acad. Sci. Inst. Math., Warsaw, 2008.
doi: 10.4064/bc81-0-7. |
[3] |
J. P. Dias, A simplified variational model for the bidimensional coupled evolution equations of a nematic liquid crystal, J. Math. Anal. Appl., 67 (1979), 525-541.
doi: 10.1016/0022-247X(79)90041-6. |
[4] |
J. P. Dias, Un problème aux limites pour un système d'équations non linéaires tridimensionnel, Bolletino, U. M. I.(5), 16 (1979), 22-31. |
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P. Grindrod, Models of individual aggregation or clustering in single and multi-species communities, J. Math. Biol., 26 (1988), 651-660.
doi: 10.1007/BF00276146. |
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O. A. Ladyzenskaja, V . A. Solonnikov and N. N. Uraltseva, Linear and Quasi-Linear Equations of Parabolic Type, Providence (R. I.) , American Mathematical Society, 1988. |
[7] |
M. Langlais and D. Phillips, Stabilization of solutions of nonlinear and degenerate evolution equations, Nonlinear Anal., 9 (1985), 321-333.
doi: 10.1016/0362-546X(85)90057-4. |
[8] |
M. Schoenauer, Quelques résultats de régularité pour un système elliptique avec conditions aux limites couplées, (French) Ann. Fac. Sci. Toulouse Math. (5), 2 (1980), 125-135.
doi: 10.5802/afst.550. |
[9] |
J. Simon, Compact sets in the space $L^p(0,T; B)$, Annali di Mathematica Pura ed Applicata (IV), 146 (1987), 65-69.
doi: 10.1007/BF01762360. |
show all references
References:
[1] |
T. Cazenave and A. Haraux, An Introduction to Semilinear Evolution Equations, Oxford Lecture Series in Mathematics and it Applications, 2006. |
[2] |
T. Cieślak, Ph. Laurençot and C. Morales-Rodrigo, Global existence and convergence to steady states in a chemorepulsion system, Parabolic and Navier-Stokes Equations, Part 1, 105-117, Banach Center Publ., 81, Part 1, Polish Acad. Sci. Inst. Math., Warsaw, 2008.
doi: 10.4064/bc81-0-7. |
[3] |
J. P. Dias, A simplified variational model for the bidimensional coupled evolution equations of a nematic liquid crystal, J. Math. Anal. Appl., 67 (1979), 525-541.
doi: 10.1016/0022-247X(79)90041-6. |
[4] |
J. P. Dias, Un problème aux limites pour un système d'équations non linéaires tridimensionnel, Bolletino, U. M. I.(5), 16 (1979), 22-31. |
[5] |
P. Grindrod, Models of individual aggregation or clustering in single and multi-species communities, J. Math. Biol., 26 (1988), 651-660.
doi: 10.1007/BF00276146. |
[6] |
O. A. Ladyzenskaja, V . A. Solonnikov and N. N. Uraltseva, Linear and Quasi-Linear Equations of Parabolic Type, Providence (R. I.) , American Mathematical Society, 1988. |
[7] |
M. Langlais and D. Phillips, Stabilization of solutions of nonlinear and degenerate evolution equations, Nonlinear Anal., 9 (1985), 321-333.
doi: 10.1016/0362-546X(85)90057-4. |
[8] |
M. Schoenauer, Quelques résultats de régularité pour un système elliptique avec conditions aux limites couplées, (French) Ann. Fac. Sci. Toulouse Math. (5), 2 (1980), 125-135.
doi: 10.5802/afst.550. |
[9] |
J. Simon, Compact sets in the space $L^p(0,T; B)$, Annali di Mathematica Pura ed Applicata (IV), 146 (1987), 65-69.
doi: 10.1007/BF01762360. |
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