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Instantaneous shrinking of the support of solutions to a nonlinear degenerate parabolic equation

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Abstract

We study the effect of shrinking of the support of a solution to a nonlinear parabolic equation with strong heat drain at low temperatures.

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References

  1. A. S. Kalashnikov, “Some problems of qualitative theory of nonlinear degenerate second order parabolic equations,”Uspekhi Mat. Nauk [Russian Math. Surveys],42, No. 2(254), 135–176 (1987).

    MATH  MathSciNet  Google Scholar 

  2. R. Kersner, “Some properties of generalized solutions to quasilinear degenerate parabolic equations,”Acta Math. Hungar.,32, 301–330 (1978).

    MATH  MathSciNet  Google Scholar 

  3. P. E. Sacks, “The initial and boundary value problem for a class of degenerate parabolic equations,”Comm. Partial Differential Equations,8, 693–733 (1983).

    MATH  MathSciNet  Google Scholar 

  4. M. A. Bertch, “A class of degenerate diffusion equations with singular term,”Nonlinear Anal.,7, 117–127 (1983).

    MathSciNet  Google Scholar 

  5. A. A. Samarskii, V. A. Galaktionov, S. P. Kurdyumov, and A. P. Mikhailov,Regimes with Peaking in the Problems for Quasilinear Parabolic Equations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  6. L. C. Evans and B. K. Knerr, “Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities,”Illinois J. Math.,23, No. 1, 153–166 (1979).

    MathSciNet  Google Scholar 

  7. A. S. Kalashnikov, “Dependence of the properties of solutions to parabolic equations in unbounded regions on the behavior of the coefficients at infinity,”Mat. Sb. [Math. USSR-Sb],125, No. 3, 398–409 (1984).

    MATH  MathSciNet  Google Scholar 

  8. B. H. Gilding and R. Kersner, “Instantaneous shrinking in nonlinear diffusion convection,”Proc. Amer. Math. Soc.,109, 385–394 (1990).

    MathSciNet  Google Scholar 

  9. A. S. Kalashnikov, “Behavior of solutions of the Cauchy problem for parabolic systems with nonliner dissipation near the initial hyperplane,”Trudy Sem. Petrovsk.,16, 106–113 (1992).

    MATH  Google Scholar 

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Authors and Affiliations

  1. M. E. Rasulzade Baku State University, USSR

    U. G. Abdullaev

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  1. U. G. Abdullaev
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Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 323–331, March, 1998.

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Abdullaev, U.G. Instantaneous shrinking of the support of solutions to a nonlinear degenerate parabolic equation. Math Notes 63, 285–292 (1998). https://doi.org/10.1007/BF02317772

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  • DOI: https://doi.org/10.1007/BF02317772

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