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View Equation

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

Equation data
Category:4. Nonlinear Partial Differential Equations
Subcategory:4.1. Second-Order Quasilinear Parabolic Equations
Equation(s):$$
\frac{\partial {w}}{\partial t} = b\frac{\partial}{\partial
x}\left\{\exp{\left[\lambda
k^2(nk+k+2)w}\right]\left( \frac{\partial {w}}{\partial
x}\right)^n\right\} + ae^{-\lambda w},\quad \ k=\frac{n+1}n.
$$
Solution(s),
Transformation(s),
Integral(s)
:
Solution:
$$
w=\lambda \ln{\left|(n+1)z\right|}, \quad\ z =
\varphi(t)\,x^{\frac{n+1}{n}} + \psi(t),
$$
where $\varphi(t)$ and $\psi(t)$ are described by
$$\begin{array}[c]{ll}
\vspace{0.1cm} \varphi(t)=\left[\cfrac{1}{C-b(n+1)^2n^{k-1}\lambda
t}\right]^{1/n}, \\ \psi(t)=-\cfrac{a\lambda
k^2}{n}t+C\cfrac{ak^3}{bn^2+n}\left(\cfrac{\lambda}{n}\right)^{2-k}.\end{array}
$$
Novelty:New equation(s) & solution(s) & transformation(s)
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Fri 25 Jan 2008 12:34
Edits by author:0

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