Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type
Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) no. 2, pp. 173-200. 
@article{AIHPC_1995__12_2_173_0,
     author = {Rodriguez, Ana and Vazquez, Juan Luis},
     title = {Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {173--200},
     publisher = {Gauthier-Villars},
     volume = {12},
     number = {2},
     year = {1995},
     mrnumber = {1326667},
     zbl = {0837.35077},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1995__12_2_173_0/}
}
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Rodriguez, Ana; Vazquez, Juan Luis. Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type. Annales de l'I.H.P. Analyse non linéaire, Tome 12 (1995) no. 2, pp. 173-200. http://archive.numdam.org/item/AIHPC_1995__12_2_173_0/

[BK] G. Bluman and S. Kumei, On the remarquable nonlinear diffusion equation ∂/∂x [a (u + b)-2(∂u/∂x)] - (∂u/∂t) = 0, J. Math. Phys., Vol. 21, 1980, pp. 1019-1023. | MR | Zbl

[C] T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz, Almqvist and Wilsell, Uppsala, 1957. | MR | Zbl

[COR] T. Chayes, S.J. Osher and J.V. Ralston, On singular diffusion equations with applications to selforganized criticality, preprint.

[DGZ] V. Van Duijn, S. Gomes and H.F. Zhang, On a class of similarity solutions of the equation ut = (um-1ux)x with m > -1, IMA J. Appl. Math., Vol. 41, 1988, pp. 147-163. | MR | Zbl

[ERV] R. Esteban, A. Rodríguez and J.L. Vazquez, A nonlinear heat equation with singular diffusivity, Comm. Partial Diff. Equations, Vol. 13, 1988, pp. 985- 1039. | MR | Zbl

[H] M.A. Herrero, A limit case in nonlinear diffusion, Nonlinear Anal., Vol. 13, 1989, pp. 611-628. | MR | Zbl

[HP] F. Hellfferich and M.C. Plesset, Ion exchange kinetics: a nonlinear diffusion problem, J. Chem. Phys., Vol. 28, 1958, pp. 418-424.

[HRP] A. Herrero and M. Pierre, The Cauchy problem for ut = Δum when 0 < m < 1, Trans. Amer. Math. Soc., Vol. 291, 1985, pp. 145-158. | Zbl

[LH] K.E. Longren and A. Hirose, Expansion of an electron cloud, Phys. Letters A, Vol. 59, 1976, pp. 285-286.

[MK] H.P. Mckean, The central limit theorem for Carleman's equation, Israel Jour. Math., Vol. 21, 1976, pp. 54-92. | MR | Zbl

[R] G. Rosen, Nonlinear heat conduction in solid H2, Phys. Rev. B, Vol. 19, 1979, pp. 2398-2399.

[RV1] A. Rodríguez and J.L. Vazquez, A well posed problem in singular Fickian diffusion, Arc. Rat. Mech Anal., Vol. 110, 1990, pp. 141-163. | MR | Zbl

[RV2] A. Rodríguez and J.L. Vazquez, Maximal solutions of singular diffusion equations with general initial data, in "Nonlinear Diffusion Equations and Their Equilibrium States", 3, N. G. LLOYD et al. eds, Birkhäuser, 1992, pp. 471-484. | MR | Zbl

[T1] P. Takáč, A fast diffusion equation which generates a monotone local semiflow I: local existence and uniqueness, Diff. Int. Eqns. | Zbl

[T2] P. Takáč, A fast diffusion equation which generates a monotone local semiflow II: global existence and asymptotic behaviour, Diff. Int. Eqns. | Zbl

[V] J.L. Vazquez, Nonexistence of solutions for nonlinear heat equations of fast-diffusion type, J. Math. Pures Appl., Vol. 71, 1992, pp. 503-526. | MR | Zbl

[VER] J.L. Vazquez, J.R. Esteban and A. Rodríguez, The fast diffusion equation with logarithmic nonlinearity and the evolution of conformal metrics in the plane, preprint, UAM Madrid, 1994. | MR

[Z] H.F. Zhang, A nonlinear singular diffusion problem: existence and uniqueness, Applicable Analysis, to appear. | MR | Zbl