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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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1 \noindent
$\displaystyle \frac{\partial w}{\partial t}=a\frac{\partial^2 w}{\partial x^2}-bw^2.$ Andrei Polyanin
Submitted: 06 Dec 06 11:22
Edited (author): 11 Dec 06 11:39
Edited (admin): 11 Dec 06 10:39
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2 \noindent
$\displaystyle \frac{\partial^2 w}{\partial t^2} +bw \frac{\partial w}{\partial t}+a\frac{\partial w}{\partial x}=0$. Yurii Kosovtsov
Submitted: 07 Dec 06 11:10
Edited (admin): 13 Dec 06 10:09
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3 $\displaystyle \frac{\partial {w}}{\partial t} = a\frac{\partial}{\partial
x}\left(w^m\frac{\partial {w}}{\partial x}\right)+bw^{1-m}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:07
Edited (admin): 23 Mar 07 10:27
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4 $\displaystyle \frac{\partial {w}}{\partial t} = a\frac{\partial}{\partial
x}\left(e^{\lambda w}\frac{\partial {w}}{\partial x}\right) +
b\,e^{-\lambda w}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:01
Edited (admin): 23 Mar 07 10:42
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5 $\displaystyle \frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left(w^{m}\frac{\partial {w}}{\partial x}\right) +
aw-bw^{1+m}+ cw^{1-m}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:19
Edited (admin): 23 Mar 07 11:04
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6 $\displaystyle \frac{\partial w}{\partial t} =
\frac{1}{r^n}\frac{\partial}{\partial
r}\left(r^n ae^{\lambda w}\frac{\partial w}{\partial r}\right) +
b\,e^{-\lambda w}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:29
Edited (admin): 23 Mar 07 11:06
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7 $\displaystyle \frac{\partial w}{\partial t} =
\frac{1}{r^n}\frac{\partial}{\partial
r}\left(r^n aw^m\frac{\partial w}{\partial r}\right) +
bw^{1-m}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:34
Edited (admin): 23 Mar 07 11:08
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8 $\displaystyle \frac{\partial w}{\partial t}=\frac12\frac{\partial^2w}{\partial x^2}+w^2(1-w)$. Konstantin Alexandrovich Volosov
Submitted: 18 Sep 07 11:50
Edited (admin): 21 Sep 07 07:10
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9 $$
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[\chi(t)\left(\alpha w^2 +\beta w +
\gamma\right)\frac{\partial {w}}{\partial x}\right] + b\theta(t).
$$ Elena Vyazmina
Submitted: 25 Jan 08 12:29
Edited (admin): 28 Jan 08 16:44
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10 $\displaystyle
\frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[\chi(t)\left(\alpha w^{1-k}+\beta w^{2-2k} +\gamma
w^{-k}\right)\frac{\partial {w}}{\partial x}\right] +
aw^{k}\theta(t).
$ Elena Vyazmina
Submitted: 25 Jan 08 12:32
Edited (admin): 28 Jan 08 16:47
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Found 17 equations, 2 pages (10 eqs. per page): << 1 2 >>

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