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List of Equations

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

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See also: Categorized List of Equations

4. Nonlinear Partial Differential Equations

4.2. Second-Order Quasilinear Hyperbolic Equations

Found 41 equations, 5 pages (10 eqs. per page): << 1 2 3 4 5 >>
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1 \noindent
$\displaystyle \left(\frac{\partial w}{\partial x}\right)^{\!2}\frac{\partial^2 w}{\partial t^2}=
\left(\frac{\partial w}{\partial t}\right)^{\!2}\frac{\partial^2 w}{\partial x^2}+
f(w)\left(\frac{\partial w}{\partial x}\right)^{\!4}$. Andrei Polyanin
Submitted: 07 Dec 06 09:08
Edited (admin): 11 Dec 06 10:50
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2 \noindent
$\displaystyle \frac{\partial^2 w}{\partial x\partial y}=\frac{\partial w}{\partial x}f\left(\frac{\partial w}{\partial x}+aw\right)$. Andrei Polyanin
Submitted: 07 Dec 06 09:21
Edited (admin): 11 Dec 06 10:56
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3 \noindent
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}=
\frac{a}{w}\left(\frac{\partial w}{\partial x}\right)^{\!2}+\frac 1w\frac{\partial w}{\partial t}\frac{\partial w}{\partial x}
+\left(b+\frac{c}{w}\right)\frac{\partial w}{\partial x}+
\frac{c}{2aw}\frac{\partial w}{\partial t}+\frac{(bw+c)^2}{4aw}$. Yurii Kosovtsov
Submitted: 11 Dec 06 10:33
Edited (admin): 11 Dec 06 15:31
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4 \noindent
$\displaystyle 
\frac{\partial^2 w}{\partial x\partial t}-\left(\frac{1}{w}\frac{\partial w}{\partial t}+b\right)
\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-
aw^2\left(c+kw+\frac{\partial w}{\partial x}\right)^{\!-1}-sw-b c = 0$. Yurii Kosovtsov
Submitted: 11 Dec 06 11:44
Edited (admin): 12 Dec 06 10:03
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5 \noindent
$\displaystyle \left( \frac{\partial^2 w}{\partial t \, \partial x} \right)^2 = \left( \frac{\partial w}{\partial x} \right)^2 \frac{\partial w}{\partial t}$ Yurii Kosovtsov
Submitted: 12 Dec 06 11:03
Edited (author): 13 Dec 06 08:36
Edited (admin): 12 Dec 06 12:30
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6 \noindent
$\displaystyle \frac{\partial^2w}{\partial t^2}=\frac{\partial}{\partial x}\left[f(w)\frac{\partial w}{\partial x}\right]$. Andrei Polyanin
Submitted: 13 Dec 06 09:52
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7 \noindent
$\displaystyle \frac{\partial^2w}{\partial t^2}=
\frac{\partial}{\partial x}\left[f(w)\frac{\partial w}{\partial x}\right]+
\frac{\partial}{\partial y}\left[g(w)\frac{\partial w}{\partial y}\right]$. Andrei Polyanin
Submitted: 13 Dec 06 09:57
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8 \noindent
$\displaystyle \frac{\partial^2w}{\partial t^2}=
\sum^n_{k=1}\frac{\partial}{\partial x_k}\left[f_k(w)\frac{\partial w}{\partial x_k}\right]$. Andrei Polyanin
Submitted: 13 Dec 06 10:00
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9 \noindent
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}
-\frac 1w\frac{\partial w}{\partial t}\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-k w= 0$.
%where $c$ and $k$ are constants. Yurii Kosovtsov
Submitted: 11 Dec 06 10:23
Edited (admin): 13 Dec 06 10:09
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10 \noindent
$\displaystyle \frac{\partial^2 w}{\partial t\partial x}-
\left(\frac 1w\frac{\partial w}{\partial t}+b\right)\frac{\partial w}{\partial x}-\frac{c}{w}\frac{\partial w}{\partial t}-c b= 0$.
%where $b$ and $c$ are constants. Yurii Kosovtsov
Submitted: 11 Dec 06 08:54
Edited (author): 11 Dec 06 12:10
Edited (admin): 13 Dec 06 10:10
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Found 41 equations, 5 pages (10 eqs. per page): << 1 2 3 4 5 >>

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