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The database contains 327 equations (8 equations are awaiting activation).

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.4. Other Second-Order Equations
Equation(s):$\displaystyle \frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[(\alpha w e^{-\lambda n
w}+\beta e^{-\lambda (n+1)w} + \gamma e^{-\lambda n w})\left( \frac{\partial {w}}{\partial
x}\right)^n\right] + b\,e^{\lambda w}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w(x,t)= -\frac{1}{\lambda}\ln{\left|\lambda (\varphi(t)\,x 
+ \psi(t))\right|}$, 
\hfill\break
where functions $\varphi(t)$ and $\psi(t)$ have the form 
$$ 
\varphi(t) = \left[\frac{1}{C_1-(n+1)\lambda^2 \beta t}\right]^
{\frac{1}{n+1}}, \quad
\psi(t) = \varphi(t)\left[\alpha \int
{\bigl[\varphi(t)\bigr]^{n}dt}+b\int{\frac{dt}{\varphi(t)}}+
C_2\right], 
$$
and $C_1$ and $C_2$ are arbitrary constants.
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 14:57
Edits by author:0

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