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Nonlinear diffusion equation and Liesegang rings. (English. Russian original) Zbl 1234.35292
Dokl. Math. 84, No. 2, 730-733 (2011); translation from Dokl. Akad. Nauk 440, No. 2, 164-167 (2011).
The authors consider the equation $$\frac{\partial u}{\partial r}=\frac{\partial^{2}u}{\partial r^{2}}+\frac{1}{r}\frac{\partial u}{\partial r}=L(u)$$, where $$L$$ is the Liesegang operator, prove that it has a solution satisfyig the condition $$u_{t=0}=\varphi$$, and study the structure of this solution.
Reviewer: Jiaqi Mo (Wuhu)

##### MSC:
 35R10 Partial functional-differential equations
##### Keywords:
diffusion equation; Liesegang ring; asymptotic expansion
Full Text:
##### References:
 [1] J. Wu, Theory and Applications of Partial Functional Differential Equations (Springer-Verlag, New York, 1996). · Zbl 0870.35116 [2] G. I. Bizhanova, Zap. Nauchn. Semin. POMI 243, 30–60 (1997). [3] R. E. Liesegang, Naturwiss. Wochenschr. 11, 353 (1896). [4] A. A. Polezhaev and S. C. Muller, Chaos 4, 631–636 (1994). [5] Ya. B. Zel’dovich, G. I. Barenblatt, and R. L. Salganik, Dokl. Akad. Nauk SSSR 140, 1281–1284 (1961).
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