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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):$\displaystyle \frac{\partial w}{\partial t} =
\frac{1}{r^n}\frac{\partial}{\partial
r}\left(r^n aw^m\frac{\partial w}{\partial r}\right) +
bw^{1-m}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w(r,t)=\left\{-\frac{mr^2}{\bigl[2m(n+1)+4\bigr]at+C}+
\frac{mb}{4m(n+1)a}\Bigl(\bigl[2m(n+1)+4\bigr]4at+C
\Bigr)\right\}^{\frac{1}{m}}$, \hfill\break
where $C$ is an 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 13:34
Edits by author:0

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