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Remarks on some dispersive estimates
A continuum of extinction rates for the fast diffusion equation
1. | Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava |
2. | Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid |
3. | Fakultät für Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany |
References:
[1] |
J. G. Berryman and C. J. Holland, Stability of the separable solution for fast diffusion, Arch. Rat. Mech. Anal., 74 (1980), 379-388.
doi: 10.1007/BF00249681. |
[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] |
J. Denzler and R. J. McCann, Fast diffusion to self-Similarity: Complete spectrum, long-time asymptotics, and numerology, Arch. Rat. Mech. Anal., 175 (2005), 301-342.
doi: 10.1007/s00205-004-0336-3. |
[6] |
M. Fila, J. King, M. Winkler and E. Yanagida, Optimal lower bound of the grow-up rate for a supercritical parabolic equation, J. Diff. Equations, 228 (2006), 339-356.
doi: 10.1016/j.jde.2006.01.019. |
[7] |
M. Fila and M. Winkler, Rate of convergence to a singular steady state of a supercritical parabolic equation, J. Evol. Equations, 8 (2008), 673-692.
doi: 10.1007/s00028-008-0400-9. |
[8] |
M. Fila, M. Winkler and E. Yanagida, Grow-up rate of solutions for a supercritical semilinear diffusion equation, J. Diff. Equations, 205 (2004), 365-389.
doi: 10.1016/j.jde.2004.03.009. |
[9] |
J. L. Vázquez, "Smoothing and Decay Estimates for Nonlinear Diffusion Equations,'' Oxford Lecture Notes in Maths. and its Applications, vol. 33, Oxford University Press, Oxford, 2006. |
[10] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory,'' Oxford Mathematical Monographs, Oxford University Press, Oxford, 2007. |
show all references
References:
[1] |
J. G. Berryman and C. J. Holland, Stability of the separable solution for fast diffusion, Arch. Rat. Mech. Anal., 74 (1980), 379-388.
doi: 10.1007/BF00249681. |
[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] |
J. Denzler and R. J. McCann, Fast diffusion to self-Similarity: Complete spectrum, long-time asymptotics, and numerology, Arch. Rat. Mech. Anal., 175 (2005), 301-342.
doi: 10.1007/s00205-004-0336-3. |
[6] |
M. Fila, J. King, M. Winkler and E. Yanagida, Optimal lower bound of the grow-up rate for a supercritical parabolic equation, J. Diff. Equations, 228 (2006), 339-356.
doi: 10.1016/j.jde.2006.01.019. |
[7] |
M. Fila and M. Winkler, Rate of convergence to a singular steady state of a supercritical parabolic equation, J. Evol. Equations, 8 (2008), 673-692.
doi: 10.1007/s00028-008-0400-9. |
[8] |
M. Fila, M. Winkler and E. Yanagida, Grow-up rate of solutions for a supercritical semilinear diffusion equation, J. Diff. Equations, 205 (2004), 365-389.
doi: 10.1016/j.jde.2004.03.009. |
[9] |
J. L. Vázquez, "Smoothing and Decay Estimates for Nonlinear Diffusion Equations,'' Oxford Lecture Notes in Maths. and its Applications, vol. 33, Oxford University Press, Oxford, 2006. |
[10] |
J. L. Vázquez, "The Porous Medium Equation. Mathematical Theory,'' Oxford Mathematical Monographs, Oxford University Press, Oxford, 2007. |
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