Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type
Annales de l'I.H.P. Analyse non linéaire, Volume 12 (1995) no. 2, p. 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},
     publisher = {Gauthier-Villars},
     volume = {12},
     number = {2},
     year = {1995},
     pages = {173-200},
     zbl = {0837.35077},
     mrnumber = {1326667},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1995__12_2_173_0}
}
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, Volume 12 (1995) no. 2, pp. 173-200. http://www.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 574874 | Zbl 0448.35027

[C] T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz, Almqvist and Wilsell, Uppsala, 1957. | MR 98477 | Zbl 0077.23401

[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 984004 | Zbl 0701.35090

[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 944437 | Zbl 0686.35066

[H] M.A. Herrero, A limit case in nonlinear diffusion, Nonlinear Anal., Vol. 13, 1989, pp. 611-628. | MR 998508 | Zbl 0682.35056

[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 0583.35052

[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 423553 | Zbl 0315.60013

[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 1037346 | Zbl 0695.76043

[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 1167857 | Zbl 0792.35084

[T1] P. Takáč, A fast diffusion equation which generates a monotone local semiflow I: local existence and uniqueness, Diff. Int. Eqns. | Zbl 0731.35059

[T2] P. Takáč, A fast diffusion equation which generates a monotone local semiflow II: global existence and asymptotic behaviour, Diff. Int. Eqns. | Zbl 0736.35059

[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 1193606 | Zbl 0694.35088

[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 1357953

[Z] H.F. Zhang, A nonlinear singular diffusion problem: existence and uniqueness, Applicable Analysis, to appear. | MR 1333950 | Zbl 0727.35074