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Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation
| 1. | Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava |
| 2. | Institut für Mathematik, Universität Paderborn, 33098 Paderborn |
References:
| [1] |
D. G. Aronson and P. Bénilan, Régularité des solutions de l'équations des milieux poreux dans $R^n$, C. R. Acad. Sci. Paris, Sér. A-B, 288 (1979), 103-105. |
| [2] |
A. Blanchet, M. Bonforte, J. Dolbeault, G. Grillo and J. L. Vázquez, Asymptotics of the fast diffusion equation via entropy estimates, Arch. Rat. Mech. Anal., 191 (2009), 347-385.
doi: 10.1007/s00205-008-0155-z. |
| [3] |
M. Bonforte, J. Dolbeault, G. Grillo and J. L. Vázquez, Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities, Proc. Nat. Acad. Sciences, 107 (2010), 16459-16464.
doi: 10.1073/pnas.1003972107. |
| [4] |
M. Bonforte, G. Grillo and J. L. Vázquez, Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold, Arch. Rat. Mech. Anal., 196 (2010), 631-680.
doi: 10.1007/s00205-009-0252-7. |
| [5] |
M. Bonforte, G. Grillo and J. L. Vázquez, Behaviour near extinction for the Fast Diffusion Equation on bounded domains, J. Math. Pures Appl., 97 (2012), 1-38.
doi: 10.1016/j.matpur.2011.03.002. |
| [6] |
M. Fila, J. R. King and M. Winkler, Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent, J. London Math. Soc., 90 (2014), 167-183.
doi: 10.1112/jlms/jdu025. |
| [7] |
M. Fila and H. Stuke, Special asymptotics for a critical fast diffusion equation, Discr. Cont. Dyn. Systems - S, 7 (2014), 725-735.
doi: 10.3934/dcdss.2014.7.725. |
| [8] |
M. Fila, J. L. Vázquez and M. Winkler, A continuum of extinction rates for the fast diffusion equation, Comm. Pure Appl. Anal., 10 (2011), 1129-1147.
doi: 10.3934/cpaa.2011.10.1129. |
| [9] |
M. Fila, J. L. Vázquez, M. Winkler and E. Yanagida, Rate of convergence to Barenblatt profiles for the fast diffusion equation, Arch. Rat. Mech. Anal., 204 (2012), 599-625.
doi: 10.1007/s00205-011-0486-z. |
| [10] |
M. Fila and M. Winkler, Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation, preprint. |
show all references
References:
| [1] |
D. G. Aronson and P. Bénilan, Régularité des solutions de l'équations des milieux poreux dans $R^n$, C. R. Acad. Sci. Paris, Sér. A-B, 288 (1979), 103-105. |
| [2] |
A. Blanchet, M. Bonforte, J. Dolbeault, G. Grillo and J. L. Vázquez, Asymptotics of the fast diffusion equation via entropy estimates, Arch. Rat. Mech. Anal., 191 (2009), 347-385.
doi: 10.1007/s00205-008-0155-z. |
| [3] |
M. Bonforte, J. Dolbeault, G. Grillo and J. L. Vázquez, Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities, Proc. Nat. Acad. Sciences, 107 (2010), 16459-16464.
doi: 10.1073/pnas.1003972107. |
| [4] |
M. Bonforte, G. Grillo and J. L. Vázquez, Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold, Arch. Rat. Mech. Anal., 196 (2010), 631-680.
doi: 10.1007/s00205-009-0252-7. |
| [5] |
M. Bonforte, G. Grillo and J. L. Vázquez, Behaviour near extinction for the Fast Diffusion Equation on bounded domains, J. Math. Pures Appl., 97 (2012), 1-38.
doi: 10.1016/j.matpur.2011.03.002. |
| [6] |
M. Fila, J. R. King and M. Winkler, Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent, J. London Math. Soc., 90 (2014), 167-183.
doi: 10.1112/jlms/jdu025. |
| [7] |
M. Fila and H. Stuke, Special asymptotics for a critical fast diffusion equation, Discr. Cont. Dyn. Systems - S, 7 (2014), 725-735.
doi: 10.3934/dcdss.2014.7.725. |
| [8] |
M. Fila, J. L. Vázquez and M. Winkler, A continuum of extinction rates for the fast diffusion equation, Comm. Pure Appl. Anal., 10 (2011), 1129-1147.
doi: 10.3934/cpaa.2011.10.1129. |
| [9] |
M. Fila, J. L. Vázquez, M. Winkler and E. Yanagida, Rate of convergence to Barenblatt profiles for the fast diffusion equation, Arch. Rat. Mech. Anal., 204 (2012), 599-625.
doi: 10.1007/s00205-011-0486-z. |
| [10] |
M. Fila and M. Winkler, Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation, preprint. |
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