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Uniqueness and stability of solutions for Cauchy problem of nonlinear diffusion equations

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Abstract

The uniqueness of solutions for Cauchy problem of the form

$$\frac{{\partial u}}{{\partial t}} = \Delta A(u) + \sum\limits_{i = 1}^N {\frac{{\partial b^i (u)}}{{\partial x_i }} + c(u)} $$

is studied. It is proved that ifu ∈BVx and A(u) is strictly increasing, the solution is unique.

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References

  1. Wu Dequan, Uniqueness of the weak solution of quasilinear degenerate parabolic equations,in Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, Vol. 3, Beijing: Science Press. 1980.

    Google Scholar 

  2. Dong Guangchang, Ye Qixiao, On the uniqueness of nonlinear degenerate parabolic equations,Chinese Annals of Math., 1982. 3 (3):279.

    MATH  Google Scholar 

  3. Chen Yazhe, Uniqueness of weak solutions of quasilinear degenerate parabolic equations, inProceedings of the 1982 Changchun Symposium on Differential Geometry and Differentia1 Equations (in Chinese), Beijing: Science Press, 317–332.

  4. Zhao Junning, Uniqueness of solutions of quasilinear degenerate parabolic equations,Northeastern Math. J. 1985, l(2): 153.

    Google Scholar 

  5. Wu Zhuoqun, Yin Jingxue, Some properties of functions in BVx and their applications to the uniqueness of solutions for degenerate quasilinear parabolic equations,Northeastern Math. J., 1989, 5 (4):389.

    Google Scholar 

  6. Brezis. H., Crandall, M. G., Uniqueness of solutions of the initial value problem for −Δϕ(u)=0 Math. Pures et Ap- Pl., 1979. 58:153.

    MATH  MathSciNet  Google Scholar 

  7. Yin Jingxue, On the uniqueness and stability of BV solutions for nonlinear diffusion equations.Comm. P.D.E., 1990, 15 (12):1671.

    Article  MATH  Google Scholar 

  8. Wu Dequan, Jiang Lishang, On the boundary value problem of a multi-dimensional quasilinear equations,Northeastern Math. J., 1985, 1 (1):54.

    MATH  Google Scholar 

  9. Zhao Junning, Uniqueness of solutions for higher dimensional quasilinear degenerate parabolic equations,Chin. Anti. of Math., 1992, 13B(2):129.

    Google Scholar 

  10. Volpert. A. I. BV spares and quasilinear equations,Math. Sb., 1967, 73:255.

    MathSciNet  Google Scholar 

  11. Wu Zhuoqun, Zhao Junning, Some general results on the first boundary value problem for quasilinear degenerate parabolic equations.Chin. Ann. of Math, 1983, 4B(3):319.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jilin University, 130023, Changchun, China

    Junning Zhao & Peidong Lei

Authors
  1. Junning Zhao
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  2. Peidong Lei
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Additional information

Project supported by the National Natural Science Foundation of China.

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Zhao, J., Lei, P. Uniqueness and stability of solutions for Cauchy problem of nonlinear diffusion equations. Sci. China Ser. A-Math. 40, 917–925 (1997). https://doi.org/10.1007/BF02878671

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  • DOI: https://doi.org/10.1007/BF02878671

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