Shrinking similar solutions of a convection diffusion equation
Authors:
Jingxue Yin and Chunpeng Wang
Journal:
Quart. Appl. Math. 62 (2004), 259-272
MSC:
Primary 35K57; Secondary 35C05, 35K15, 76M55, 76S05
DOI:
https://doi.org/10.1090/qam/2054599
MathSciNet review:
MR2054599
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Abstract: In this paper we study the convection diffusion equation \[ \frac {{\partial u}}{{\partial t}} = \Delta {u^m} - x \cdot \nabla {u^q}, \qquad (x, t) \in {\mathbb {R}{^n}} \times (0, + \infty )\], where $m > 1, 1 < q \le m$.
- A. S. Kalashnikov, Some problems of the qualitative theory of second-order nonlinear degenerate parabolic equations, Uspekhi Mat. Nauk 42 (1987), no. 2(254), 135–176, 287 (Russian). MR 898624
- Andrey Shishkov, Instantaneous shrinking phenomenon for solutions of higher-dimensional nonlinear diffusion-convection equations, Methods Funct. Anal. Topology 5 (1999), no. 3, 54–76. MR 1771546
- Ugur G. Abdullaev, Instantaneous shrinking and exact local estimations of solutions in nonlinear diffusion absorption, Adv. Math. Sci. Appl. 8 (1998), no. 1, 483–503. MR 1623323
- B. H. Gilding and R. Kersner, Instantaneous shrinking in nonlinear diffusion-convection, Proc. Amer. Math. Soc. 109 (1990), no. 2, 385–394. MR 1007496, DOI https://doi.org/10.1090/S0002-9939-1990-1007496-9
A. S. Kalashnikov, Some problems of the qualitative theory of nonlinear degenerate second order parabolic equations, Russian Math. Surveys, 42(2)(1987), 169–222.
A. Shishkov, Instantaneous shrinking phenomenon for solutions of higher-dimensional nonlinear diffusion-convection equations, Methods Funct. Anal., Topology, 5(3)(1999), 54–76.
U. G. Abdullaev, Instantaneous shrinking and exact local estimations of solutions in nonlinear diffusion absorption, Adv. Math. Sci. Appl., 8(1)(1998), 483–503.
B. H. Gilding and R. Kersner, Instantaneous shrinking in nonlinear diffusion-convection, Proc. Amer. Math. Soc., 109(2)(1990), 385–394.
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© Copyright 2004
American Mathematical Society
