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List of Equations

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

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4. Nonlinear Partial Differential Equations

4.1. Second-Order Quasilinear Parabolic Equations

Found 17 equations, 2 pages (10 eqs. per page): << 1 2 >>
 Equation(s)Author/
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11 $\displaystyle
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[\chi(t)\left(\alpha w +\beta e^{\lambda w} +\gamma
e^{-\lambda w}\right)\frac{\partial {w}}{\partial x}\right] +
ae^{\lambda w}\theta(t)$. Elena Vyazmina
Submitted: 25 Jan 08 12:33
Edited (admin): 28 Jan 08 16:49
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12 $\displaystyle
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[\chi(t)f({w})\frac{\partial {w}}{\partial x}\right] +
g(w)\theta(t).
$ Elena Vyazmina
Submitted: 25 Jan 08 12:28
Edited (admin): 28 Jan 08 17:01
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13 $$
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[\chi(t)\left(\frac{\alpha w}{aw+b} +\beta
\frac{\ln{\left|aw+b\right|}-1}{aw+b} + \frac{
\gamma}{aw+b}\right)\frac{\partial {w}}{\partial x}\right] +
(aw+b)\theta(t).
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:30
Edited (admin): 29 Jan 08 14:33
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14 $$
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[\chi(t)\left(\frac{\alpha w+\gamma}{(aw+b)^2}
+\frac{\beta}{(aw+b)^2} \ln{\left|aw+b\right|} \right)\frac{\partial {w}}{\partial x}\right] +
(aw+b)^2\theta(t).
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:31
Edited (admin): 29 Jan 08 14:37
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15 $$
\frac{\partial {w}}{\partial t} = b\frac{\partial}{\partial
x}\left\{\exp{\left[\lambda
k^2(nk+k+2)w}\right]\left( \frac{\partial {w}}{\partial
x}\right)^n\right\} + ae^{-\lambda w},\quad \ k=\frac{n+1}n.
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:34
Edited (admin): 29 Jan 08 14:42
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16 $$
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[f({w})\left( \frac{\partial {w}}{\partial
x}\right)^n\right] + g(w).
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:34
Edited (admin): 29 Jan 08 15:23
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17 $\displaystyle \frac{\partial w}{\partial t}+w\frac{\partial w}{\partial x}-
a\frac{\partial^2 w}{\partial x^2}=-f(x,t)$.\quad \ The generalized Burgers equation. Andrei Polyanin
Submitted: 25 Feb 09 13:31
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Found 17 equations, 2 pages (10 eqs. per page): << 1 2 >>

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