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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:4.4. Other Second-Order Equations
Equation(s):$$
\frac{\partial {w}}{\partial t} = A\frac{\partial}{\partial
x}\left\{ {w}^{\frac{(n+1)^2-\lambda(n+n^2)-2n^2}
{n^2(n+1)}}\left(\frac{\partial {w}}{\partial x}\right)^n\right\} + 
B {w}^{\lambda}.
$$
Solution(s),
Transformation(s),
Integral(s)
:
Solution:
$$
w=\left[(n+1)z\right]^{\frac{1}{1-\lambda}}, \quad\ z =
\varphi(t)\,x^{\frac{n+1}{n}} + \psi(t),
$$
where the functions $\varphi(t)$ and $\psi(t)$ are described by
$$\begin{array}[c]{ll}
\vspace{0.1cm} \varphi(t)=\left[\cfrac{1}{C-A(n+1)^n(k+1-\lambda)
(1-\lambda)^{-n}nk^n t}\right]^{1/n},\\
\psi(t)=\cfrac{n k B}{n^2(k+2-2\lambda)}t-
\cfrac{(1-\lambda)^n k^{n+1} B
C}{n^2(n+1)^n(k+2-2\lambda)(k+1-\lambda)A},
\end{array}
$$
and $k=(n+1)/n$.
Novelty:New equation(s) & solution(s) & transformation(s)
Author/Contributor's Details
Last name:Vyazmina
First name:Elena
Middle(s) name:Andreevna
Country:Russia
City:Moscow
Affiliation:Institute for Problems in Mechanics
Statistic information
Submission date:Fri 25 Jan 2008 12:36
Edits by author:1
Last edit by author:Sat 12 Apr 2008 14:49

Edit (Only for author/contributor)


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