Regularity analysis for systems of reaction-diffusion equations

 Access to full text

1. [1] J. M. Ball, On the asymptotic behavior of generalized processes, with applications to nonlinear evolution equations, J. Differential Equations27 (1978), 224–265. Zbl0376.35002MR461576
2. [2] M. Bisi & L. Desvillettes, From reactive Boltzmann equations to reaction–diffusion systems, J. Stat. Phys.124 (2006), 881–912. Zbl1134.82323MR2264629
3. [3] H. Brezis, Analyse fonctionnelle. Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, Masson, 1983. Zbl0511.46001MR697382
4. [4] L. Caffarelli, R. V. Kohn & L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math.35 (1982), 771–831. Zbl0509.35067MR673830
5. [5] L. Caffarelli & A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, to appear in Annals of Math.. Zbl1204.35063MR2680400
6. [6] J.-F. Collet, Some modelling issues in the theory of fragmentation-coagulation systems, Commun. Math. Sci.2 (2004), 35–54. Zbl1153.82328MR2119872
7. [7] E. De Giorgi, Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat.3 (1957), 25–43. Zbl0084.31901MR93649
8. [8] L. Desvillettes & K. Fellner, Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations, J. Math. Anal. Appl.319 (2006), 157–176. Zbl1096.35018MR2217853
9. [9] L. Desvillettes & K. Fellner, Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds, Rev. Mat. Iberoam.24 (2008), 407–431. Zbl1171.35330MR2459198
10. [10] L. Desvillettes, K. Fellner, M. Pierre & J. Vovelle, About global existence for quadratic systems of reaction-diffusion, J. Advanced Nonlinear Studies7 (2007), 491–511. Zbl1330.35211MR2340282
11. [11] P. Erdi & J. Tóth, Mathematical models of chemical reactions, Nonlinear Science: Theory and Applications, Manchester Univ. Press, 1989. Zbl0696.92027MR981593
12. [12] H. Federer, Geometric measure theory, Die Grund. Math. Wiss., Band 153, Springer New York Inc., New York, 1969. Zbl0176.00801MR257325
13. [13] W. Feng, Coupled system of reaction–diffusion equations and applications in carrier facilitated diffusion, Nonlinear Anal.17 (1991), 285–311. Zbl0772.35030MR1120978
14. [14] P. C. Fife, Mathematical aspects of reacting and diffusing systems, Lecture Notes in Biomath. 28, Springer, 1979. Zbl0403.92004MR527914
15. [15] Y. Giga & R. V. Kohn, Asymptotically self-similar blow-up of semilinear heat equations, Comm. Pure Appl. Math.38 (1985), 297–319. Zbl0585.35051MR784476
16. [16] O. A. Ladyzenskaia, V. A. Solonnikov & N. N. Uralceva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monographs 23, AMS, 1968. Zbl0174.15403
17. [17] F. Lin, A new proof of the Caffarelli–Kohn–Nirenberg theorem, Comm. Pure and Appl. Math.51 (1998), 241–257. Zbl0958.35102MR1488514
18. [18] A. Mellet & A. Vasseur, $L^p$ estimates for quantities advected by a compressible flow, J. Math. Anal. Appl.355 (2009), 548–563. Zbl1172.35056MR2521733
19. [19] J. Morgan, Global existence for semilinear parabolic systems, SIAM J. Math. Anal.20 (1989), 1128–1144. Zbl0692.35055MR1009350
20. [20] J. Morgan, Global existence for semilinear parabolic systems via Lyapunov type methods, in Nonlinear semigroups, partial differential equations and attractors (Washington, DC, 1987), Lecture Notes in Math. 1394, Springer, 1989, 117–121. Zbl0688.35038MR1021018
21. [21] J. Morgan, Boundedness and decay results for reaction-diffusion systems, SIAM J. Math. Anal.21 (1990), 1172–1189. Zbl0723.35039MR1062398
22. [22] J. Morgan, On a question of blow-up for semilinear parabolic systems, Differential Integral Equations3 (1990), 973–978. Zbl0747.35012MR1059344
23. [23] J. Morgan & S. Waggonner, Global existence for a class of quasilinear reaction-diffusion systems, Commun. Appl. Anal.8 (2004), 153–166. Zbl1122.35058MR2055878
24. [24] J. D. Murray, Mathematical biology, Interdisciplinary Applied Math. 17 & 18, Springer, 2003. Zbl0682.92001MR1952568
25. [25] M. Pierre, Weak solutions and supersolutions in $L^1$ for reaction-diffusion systems, J. Evol. Equ.3 (2003), 153–168. Zbl1026.35047MR1977432
26. [26] M. Pierre & D. Schmitt, Blowup in reaction-diffusion systems with dissipation of mass, SIAM Rev. 42 (2000), 93–106 (electronic). Zbl0942.35033MR1738101
27. [27] M. Pierre & R. Texier-Picard, Global existence for degenerate quadratic reaction-diffusion systems, to appear in Ann. IHP Anal. non linéaire. Zbl1180.35288MR2566699
28. [28] F. Rothe, Global solutions of reaction–diffusion systems, Lecture Notes in Math. 102, Springer, 1984. Zbl0546.35003MR755878
29. [29] V. Scheffer, Partial regularity of solutions to the Navier-Stokes equations, Pacific J. Math.66 (1976), 535–552. Zbl0325.35064MR454426
30. [30] V. Scheffer, Hausdorff measure and the Navier-Stokes equations, Comm. Math. Phys.55 (1977), 55–97. Zbl0357.35071MR510154
31. [31] L. W. Somathilake & J. M. J. J. Peiris, Global solutions of a strongly coupled reaction-diffusion system with different diffusion coefficients, J. Appl. Math.1 (2005), 23–36. Zbl1175.35076MR2144501
32. [32] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton Univ. Press, 1970. Zbl0207.13501
33. [33] A. Vasseur, A new proof of partial regularity of solutions to Navier-Stokes equations, NoDEA Nonlinear Differential Equations Appl.14 (2007), 753–785. Zbl1142.35066
34. [34] C. Villani, Hypocoercive diffusion operators, in Proceedings of the International Congress of Mathematicians, 2006. Zbl1130.35027
35. [35] F. B. Weissler, An $L^{\infty }$ blow-up estimate for a nonlinear heat equation, Comm. Pure Appl. Math.38 (1985), 291–295. Zbl0592.35071