Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type

Ana Rodriguez; Juan Luis Vazquez

Annales de l'I.H.P. Analyse non linéaire (1995)

  • Volume: 12, Issue: 2, page 173-200
  • ISSN: 0294-1449

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Rodriguez, Ana, and Vazquez, Juan Luis. "Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type." Annales de l'I.H.P. Analyse non linéaire 12.2 (1995): 173-200. <http://eudml.org/doc/78357>.

@article{Rodriguez1995,
author = {Rodriguez, Ana, Vazquez, Juan Luis},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {non-uniqueness; infinitely many solutions; fast diffusion},
language = {eng},
number = {2},
pages = {173-200},
publisher = {Gauthier-Villars},
title = {Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type},
url = {http://eudml.org/doc/78357},
volume = {12},
year = {1995},
}

TY - JOUR
AU - Rodriguez, Ana
AU - Vazquez, Juan Luis
TI - Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 2
SP - 173
EP - 200
LA - eng
KW - non-uniqueness; infinitely many solutions; fast diffusion
UR - http://eudml.org/doc/78357
ER -

References

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  2. [C] T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz, Almqvist and Wilsell, Uppsala, 1957. Zbl0077.23401MR98477
  3. [COR] T. Chayes, S.J. Osher and J.V. Ralston, On singular diffusion equations with applications to selforganized criticality, preprint. Zbl0832.35142
  4. [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 &gt; -1, IMA J. Appl. Math., Vol. 41, 1988, pp. 147-163. Zbl0701.35090MR984004
  5. [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. Zbl0686.35066MR944437
  6. [H] M.A. Herrero, A limit case in nonlinear diffusion, Nonlinear Anal., Vol. 13, 1989, pp. 611-628. Zbl0682.35056MR998508
  7. [HP] F. Hellfferich and M.C. Plesset, Ion exchange kinetics: a nonlinear diffusion problem, J. Chem. Phys., Vol. 28, 1958, pp. 418-424. 
  8. [HRP] A. Herrero and M. Pierre, The Cauchy problem for ut = Δum when 0 &lt; m &lt; 1, Trans. Amer. Math. Soc., Vol. 291, 1985, pp. 145-158. Zbl0583.35052
  9. [LH] K.E. Longren and A. Hirose, Expansion of an electron cloud, Phys. Letters A, Vol. 59, 1976, pp. 285-286. 
  10. [MK] H.P. Mckean, The central limit theorem for Carleman's equation, Israel Jour. Math., Vol. 21, 1976, pp. 54-92. Zbl0315.60013MR423553
  11. [R] G. Rosen, Nonlinear heat conduction in solid H2, Phys. Rev. B, Vol. 19, 1979, pp. 2398-2399. 
  12. [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. Zbl0695.76043MR1037346
  13. [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. Zbl0792.35084MR1167857
  14. [T1] P. Takáč, A fast diffusion equation which generates a monotone local semiflow I: local existence and uniqueness, Diff. Int. Eqns. Zbl0731.35059
  15. [T2] P. Takáč, A fast diffusion equation which generates a monotone local semiflow II: global existence and asymptotic behaviour, Diff. Int. Eqns. Zbl0736.35059
  16. [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. Zbl0694.35088MR1193606
  17. [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, UAMMadrid, 1994. MR1357953
  18. [Z] H.F. Zhang, A nonlinear singular diffusion problem: existence and uniqueness, Applicable Analysis, to appear. Zbl0727.35074MR1333950

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