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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):$\displaystyle
\frac{\partial w}{\partial t} = a
\biggl(\frac{\partial w}{\partial x}\biggr)^m \frac{\partial^2 w}{\partial x^2}.
$
Solution(s),
Transformation(s),
Integral(s)
:
1. Solution:
$$
w(x,t) = aA^{m+1}t  + B +
A\frac{\left[x(m+1)+mC_1+C_1\right]^{1+\frac{1}{m+1}}}{m+2}+C_2,
$$
where $A$, $B$, and $C$ are arbitrary constants.
\medskip

2. Solution:
$$
w(x,t)=-ap_1t+A + \frac{2ap_1p_2t+B}{p_2+p_1e^{p_1x}},
$$
where $A$, $B$, $p_1$, and $p_2$ are arbitrary constants.
\medskip

3. Solution:
$$
w(x,t)=At+B+Ce^{A/ax},
$$
where $A$, $B$, and $C$ are arbitrary constants.
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 12:44
Edits by author:0

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