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Special asymptotics for a critical fast diffusion equation
1. | Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava |
2. | Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany |
References:
[1] |
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,, Nat. Bureau of Standards, (1964).
|
[2] |
J. G. Berryman and C. J. Holland, Stability of the separable solution for fast diffusion,, Arch. Rat. Mech. Anal., 74 (1980), 379.
doi: 10.1007/BF00249681. |
[3] |
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.
doi: 10.1007/s00205-008-0155-z. |
[4] |
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.
doi: 10.1073/pnas.1003972107. |
[5] |
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.
doi: 10.1007/s00205-009-0252-7. |
[6] |
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.
doi: 10.1016/j.matpur.2011.03.002. |
[7] |
P. Daskalopoulos and N. Sesum, On the extinction profile of solutions to fast diffusion,, J. Reine Angew. Math., 622 (2008), 95.
doi: 10.1515/CRELLE.2008.066. |
[8] |
M. del Pino and M. Sáez, On the extinction profile for solutions of $u_t=\Delta u^{(N-2)/(N+2)}$,, Indiana Univ. Math. J., 50 (2001), 611.
doi: 10.1512/iumj.2001.50.1876. |
[9] |
E. Feireisl and F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions,, J. Dyn. Diff. Eq., 12 (2000), 647.
doi: 10.1023/A:1026467729263. |
[10] |
M. Fila, J. R. King and M. Winkler, Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent,, preprint, (). Google Scholar |
[11] |
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.
doi: 10.3934/cpaa.2011.10.1129. |
[12] |
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.
doi: 10.1007/s00205-011-0486-z. |
[13] |
M. Fila and M. Winkler, Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation,, preprint., (). Google Scholar |
[14] |
V. A. Galaktionov and L. A. Peletier, Asymptotic behaviour near finite-time extinction for the fast diffusion equation,, Arch. Rat. Mech. Anal., 139 (1997), 83.
doi: 10.1007/s002050050048. |
[15] |
J. R. King, Self-similar behaviour for the equation of fast nonlinear diffusion,, Phil. Trans. Roy. Soc. Lond. A, 343 (1993), 337.
doi: 10.1098/rsta.1993.0052. |
[16] |
M. A. Peletier and H. Zhang, Self-similar solutions of a fast diffusion equation that do not conserve mass,, Diff. Int. Equations, 8 (1995), 2045.
|
[17] |
J. L. Vázquez, Smoothing and Decay Estimates for Nonlinear Diffusion Equations,, Oxford Lecture Notes in Maths. and its Applications, (2006).
doi: 10.1093/acprof:oso/9780199202973.001.0001. |
show all references
References:
[1] |
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,, Nat. Bureau of Standards, (1964).
|
[2] |
J. G. Berryman and C. J. Holland, Stability of the separable solution for fast diffusion,, Arch. Rat. Mech. Anal., 74 (1980), 379.
doi: 10.1007/BF00249681. |
[3] |
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.
doi: 10.1007/s00205-008-0155-z. |
[4] |
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.
doi: 10.1073/pnas.1003972107. |
[5] |
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.
doi: 10.1007/s00205-009-0252-7. |
[6] |
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.
doi: 10.1016/j.matpur.2011.03.002. |
[7] |
P. Daskalopoulos and N. Sesum, On the extinction profile of solutions to fast diffusion,, J. Reine Angew. Math., 622 (2008), 95.
doi: 10.1515/CRELLE.2008.066. |
[8] |
M. del Pino and M. Sáez, On the extinction profile for solutions of $u_t=\Delta u^{(N-2)/(N+2)}$,, Indiana Univ. Math. J., 50 (2001), 611.
doi: 10.1512/iumj.2001.50.1876. |
[9] |
E. Feireisl and F. Simondon, Convergence for semilinear degenerate parabolic equations in several space dimensions,, J. Dyn. Diff. Eq., 12 (2000), 647.
doi: 10.1023/A:1026467729263. |
[10] |
M. Fila, J. R. King and M. Winkler, Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent,, preprint, (). Google Scholar |
[11] |
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.
doi: 10.3934/cpaa.2011.10.1129. |
[12] |
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.
doi: 10.1007/s00205-011-0486-z. |
[13] |
M. Fila and M. Winkler, Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation,, preprint., (). Google Scholar |
[14] |
V. A. Galaktionov and L. A. Peletier, Asymptotic behaviour near finite-time extinction for the fast diffusion equation,, Arch. Rat. Mech. Anal., 139 (1997), 83.
doi: 10.1007/s002050050048. |
[15] |
J. R. King, Self-similar behaviour for the equation of fast nonlinear diffusion,, Phil. Trans. Roy. Soc. Lond. A, 343 (1993), 337.
doi: 10.1098/rsta.1993.0052. |
[16] |
M. A. Peletier and H. Zhang, Self-similar solutions of a fast diffusion equation that do not conserve mass,, Diff. Int. Equations, 8 (1995), 2045.
|
[17] |
J. L. Vázquez, Smoothing and Decay Estimates for Nonlinear Diffusion Equations,, Oxford Lecture Notes in Maths. and its Applications, (2006).
doi: 10.1093/acprof:oso/9780199202973.001.0001. |
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