Pacific Journal of Mathematics

On the Cauchy problem for a singular parabolic equation.

Xiangsheng Xu

Article information

Pacific J. Math., Volume 174, Number 1 (1996), 277-294.

First available in Project Euclid: 6 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K65: Degenerate parabolic equations
Secondary: 35K55: Nonlinear parabolic equations


Xu, Xiangsheng. On the Cauchy problem for a singular parabolic equation. Pacific J. Math. 174 (1996), no. 1, 277--294.

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  • [BM] L.Boccardo and F. Murat, Almost everywhereconvergenceofthe gradients ofso- lutions to elliptic and parabolic equations, Nonlinear Anal., 19(1992), 581-597.
  • [BGDM] L. Boccardo, T. Gallouet, J.I. Diaz and F. Murat, Existence and regularityofrenor- malizedsolutionsforsome ellipticproblemsinvolving derivatives ofnonlinear terms, J. Differential equations, toappear.
  • [D] E. DiBenedetto, Degenerate Parabolic Equations, Springer-Verlag, New York, 1993.
  • [DH] E. DiBenedetto and M.A. Herrero, Non-negative solutions of the evolution p-Laplaci- an equation,initial traces, and Cauchyproblemwhen1 < p < 2, Arch. Rat. Mech. Anal., I l l (1990), 225-290.
  • [DL1] R.J. DiPerna and P.L. Lions, Globaleexistencefor the Fokker-Planck-Boltzmann equations,Comm. Pure Appl. Math., 11 (1989), 729-758.
  • [DL2] R.J. DiPerna and P.L. Lions, On the Cauchy problemfor Boltzmann equations: globale existenceand weakstability,Ann. Math., 130 (1989), 321-366.
  • [LSU] O.A. Ladyzenskaya,V.A. Solonnikov and N.N. Uralceva, Linear andQuasilinear equationsof ParabolicType,AMS,Rhode Island, 1968.
  • [O] J.T. Oden, Qualitative Methodsin NonlinearMechanics, Prentice-Hall, Inc., New Jersey, 1986.
  • [S] J. Simon, Compactsets in the spaceZ/(0, T,B), Am. Mat. Pura Appl., 146 (1987), 65-96.
  • [XI] X. Xu, On the initial-boundary-value problem for ut --div (|Vt|p~2 Vu) = 0, Arch. Rational Mech. Anal., 127 (1994), 337-360.
  • [X2] T. Kilpelainen and X. Xu, On the uniquenessproblemfor quasilinearelliptic equa- tions involving measures,Revista Mat. Iberoamericana, 12 (1996), to appear.