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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):$\displaystyle \frac{\partial w}{\partial t} =
\frac{1}{r^n}\frac{\partial}{\partial
r}\left(r^n ae^{\lambda w}\frac{\partial w}{\partial r}\right) +
b\,e^{-\lambda w}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w(r,t)=\frac{1}{\lambda}\ln{\left|\frac{r^2}{C-2\left(n+1\right)at}
+\frac{b\lambda}{4(n+1)a}\bigl[2\left(n+1\right)at-C\bigr]\right|}$,\hfill\break
where $C$ is arbitrary constant.
Novelty:Material has been fully published elsewhere
References:E. A. Vyazmina and A. D. Polyanin, Theoretical Foundations of Chemical Engineering, 2006, Vol. 40, No. 6, pp. 555563.
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Middle(s) name:Andreevna
Country:Russia
City:Moscow
Affiliation:Ph.D student of Institute for Problems in Mechanics, Russian Academy of Sciences
Statistic information
Submission date:Thu 21 Dec 2006 13:29
Edits by author:0

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