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This work addresses the {\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\em cylindrical behavior at infinity}.
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Galaktionov, V.,A., Posaskov, S.,A. On the nonlinear ”fast diffusion” equation in ℝ N \mathbb{R}^{N}
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King, J.R., Self-similar behavior for the equation of fast nonlinear diffusion, phil. Trans. R. Soc., London, A 343
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Ye, R., Global existence and convergence of Yamabe flow. J. Differential Geom. 39 (1994), no. 1, 35–50
1994
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Galaktionov, V.,A., Peletier, L.A, Asymptotic Behaviour near Finite-Time Extinction of the Fast-Diffusion Equation
1997
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King, J.R., Extremely high concentration dopant diffusion in silicon, IMA J. Appl. Math. 40 (1998) 163–181
1998
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del Pino, M.; Sáez, M., On the extinction profile for solutions of u t = Δ u ( N − 2 ) / ( N + 2 ) u_{t}=\Delta u^{(N-2)/(N+2)}
2001
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Brendle, S., Convergence of the Yamabe flow for arbitrary initial energy
2005
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Carron, G., Herzlich, M., Conformally flat manifolds with non negative Ricci curvature
2006
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Vázquez, J. L., Smoothing and decay estimates for nonlinear diffusion equations
2006
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Brendle, S., Convergence of the Yamabe flow in dimension 6 and higher
2007
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Carrillo, J.A., Di Francesco, M., Toscani, G., Strict concavity of the 2-Wasserstein distance for the porous medium equation by mass-centering
2007
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Daskalopoulos, P., Kenig, C. E., Degenerate diffusions: Initial Value Problems and Local Regularity Theory
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Chasseigne, E.,Vazquez, J.L., Theory of extended solutions for fast-diffusion equations in optimal classes of data
2002
Cited alongside, same era.
Hsu, S.-Y., Asymptotic profile of solutions of a singular diffusion equation as t → ∞ t\to\infty
2002
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Schwetlick, H.; Struwe, M. Convergence of the Yamabe flow for ”large” energies
2003
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Vazquez,J.L., Asymptotic behaviour for the porous medium equation posed in the whole space
2003
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Cao, H.-D., Sun, X., Zhang, Y., On the structure of gradient Yamabe solitons
Cited in the paper.
Cited in the paper.
Daskalopoulos, P., Sesum, N., Classification of conformally flat Yamabe solitons
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2007
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Daskalopoulos, P., Sesum, N., On the extinction profile of solutions to fast diffusion
2008
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Blanchet, A., Bonforte, M., Dolbeault, J., Grillo, G., Vaźquez, J.L., Asymptotics of the fast diffusion equation via entropy estimates
2009
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Peletier, M.A. and Zhang, H., Self-similar solutions of the fast-diffusion equation that do not conserve mass
2064
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