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Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):$\displaystyle \frac{\partial {w}}{\partial t} = a\frac{\partial}{\partial
x}\left(e^{\lambda w}\frac{\partial {w}}{\partial x}\right) +
b\,e^{-\lambda w}$.
Solution(s),
Transformation(s),
Integral(s)
:
Solution:\hfill\break
$\displaystyle w(x,t)=\frac{1}{\lambda}\ln{\left|\frac{(x+C_1)^2}{C_2-2at}+
\frac{b\lambda}{4a}\left(2at-C_2\right)\right|}$,\hfill\break
where $C_1$ 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
Statistic information
Submission date:Thu 21 Dec 2006 13:01
Edits by author:0

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