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A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION
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 Title & Authors
A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION
Fang, Zhong Bo;
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 Abstract
We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: $$[\mid(w^m)]`\mid^{p-2}(w^m)`]`\;+\;{\beta}rw`\;+\;{\alpha}w\;+\;(w^q)`\;
 Keywords
very singular solution;existence;uniqueness;asymptotic behavior;
 Language
English
 Cited by
 References
1.
J. S. Baek, M. Kwak, and K. Yu, Uniqueness of the very singular solution of a degenerate parabolic equation, Nonlinear Anal. 45 (2001), no. 1, Ser. A: Theory Methods, 123-135. crossref(new window)

2.
P. Biler and G. Karch, A Neumann problem for a convection-diffusion equation on the half-line, Ann. Polon. Math. 74 (2000), 79-95.

3.
H. Brezis, L. A. Peletier, and D. Terman, A very singular solution of the heat equation with absorption, Arch. Rational Mech. Anal. 95 (1986), no. 3, 185-209.

4.
J. L. Diaz and J. E. Saa, Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption, Publ. Mat. 36 (1992), no. 1, 19-38. crossref(new window)

5.
E. DiBenedetto, Degenerate Parabolic Equations, Springer-Verlag, New York, 1993.

6.
M. Escobedo, O. Kavian, and H. Matano, Large time behavior of solutions of a dissipative semilinear heat equation, Comm. Partial Differential Equations 20 (1995), no. 7-8, 1427-1452. crossref(new window)

7.
M. Escobedo and E. Zuazua, Large time behavior for convection-diffusion equations in $R^N$, J. Funct. Anal. 100 (1991), no. 1, 119-161. crossref(new window)

8.
M. Escobedo, J. L. Vazquez, and E. Zuazua, A diffusion-convection equation in several space dimensions, Indiana Univ. Math. J. 42 (1993), no. 4, 1413-1440. crossref(new window)

9.
L. C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, 1998.

10.
Z. B. Fang and M. Kwak, Complete classification of shape functions of self-similar solutions, J. Math. Anal. Appl. 330 (2007), no. 2, 1447-1464. crossref(new window)

11.
M. Guedda, Self-similar solutions to a convection-diffusion processes, Electron. J. Qual. Theory Differ. Equ. 2000 (2000), no. 3, 17 pp.

12.
S. Kamin and L. Veron, Existence and uniqueness of the very singular solution of the porous media equation with absorption, J. Analyse Math. 51 (1988), 245-258. crossref(new window)

13.
M. Kwak, A semilinear heat equation with singular initial data, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 4, 745-758.

14.
M. Kwak, A porous media equation with absorption. II. Uniqueness of the very singular solution, J. Math. Anal. Appl. 223 (1998), no. 1, 111-125.

15.
M. Kwak, A porous media equation with absorption. I. Long time behaviour, J. Math. Anal. Appl. 223 (1998), no. 1, 96-110. crossref(new window)

16.
M. Kwak and K. Yu, Asymptotic behaviour of solutions of a degenerate parabolic equation, Nonlinear Anal. 45 (2001), no. 1, Ser. A: Theory Methods, 109-121. crossref(new window)

17.
Ph. Laurencot and F. Simondon, Source-type solutions to porous medium equations with convection, Commun. Appl. Anal. 1 (1997), no. 4, 489-502.

18.
Ph. Laurencot and F. Simondon, Long-time behaviour for porous medium equations with convection, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), no. 2, 315-336.

19.
G. Leoni, On the existence of fast-decay solutions for a quasilinear elliptic equation with a gradient term, Atti Sem. Mat. Fis. Univ. Modena 46 (1998), suppl., 827-846.

20.
L. A. Peletier and H. C. Serafini, A very singular solution and other self-similar solutions of the heat equation with convection, Nonlinear Anal. 24 (1995), no. 1, 29-49. crossref(new window)

21.
L. A. Peletier and D. Terman, A very singular solution of the porous media equation with absorption, J. Differential Equations 65 (1986), no. 3, 396-410. crossref(new window)

22.
L. A. Peletier and J.Wang, A very singular solution of a quasilinear degenerate diffusion equation with absorption, Trans. Amer. Math. Soc. 307 (1988), no. 2, 813-826. crossref(new window)

23.
Z. Q. Wu, J. N. Zhao, J. X. Yin, and H. L. Li, Nonlinear Diffusion Equations, WorldScientific Publishing Co., Inc., River Edge, NJ, 2001.

24.
J. N. Zhao, The asymptotic behaviour of solutions of a quasilinear degenerate parabolic equation, J. Differential Equations 102 (1993), no. 1, 33-52. crossref(new window)