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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

4.4. Other Second-Order Equations

Found 106 equations, 11 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 >>
 Equation(s)Author/
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91 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\left(\frac{\partial w}{\partial x}+a\frac{\partial w}{\partial y}+a^2
\right)\frac{\partial^2 w}{\partial y^2}-
\left(\frac{\partial w}{\partial y}+a\right)^2=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:27
Edited (admin): 11 Jan 08 09:33
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92 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}+
F\left(y,\frac{\partial w}{\partial y}\right)\frac{\partial^2 w}{\partial x\partial y}=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:16
Edited (admin): 11 Jan 08 09:35
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93 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
(y+a)^{-2}\left(\frac{\partial w}{\partial x}+b\right)^2=0$.\hfill\break Valentin Zaitsev
Submitted: 05 Sep 07 13:13
Edited (admin): 11 Jan 08 09:36
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94 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
\frac{(\beta_1-\beta_2)^2(\frac{\partial w}{\partial x}+\alpha_1)^2
(\frac{\partial w}{\partial x}+\alpha_2)^2}
{(\alpha_1-\alpha_2)^2(y+\beta_1)^2(y+\beta_2)^2}=0$.\hfill\break Valentin Zaitsev
Submitted: 04 Sep 07 18:08
Edited (admin): 11 Jan 08 09:36
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95 $\displaystyle \left(\frac{\partial^2 w}{\partial x\partial y}\right)^2-
\frac{\partial^2 w}{\partial x^2}\frac{\partial^2 w}{\partial y^2}-
a^2\left(\frac{\partial w}{\partial x}+b\right)^4=0$.\hfill\break Valentin Zaitsev
Submitted: 04 Sep 07 18:05
Edited (admin): 11 Jan 08 09:37
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96 $\displaystyle \frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left[(\alpha w e^{-\lambda n
w}+\beta e^{-\lambda (n+1)w} + \gamma e^{-\lambda n w})\left( \frac{\partial {w}}{\partial
x}\right)^n\right] + b\,e^{\lambda w}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 14:57
Edited (admin): 11 Jan 08 09:41
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97 \noindent
$\displaystyle \frac{\partial^2w}{\partial t\partial x} = \left (\frac{\partial w}{\partial t}+aw\right )\frac{\partial^2w}{\partial x^2}\left ( \frac{\partial w}{\partial x} \right )^{-1} -a \frac{\partial w}{\partial x}+f(x)\left ( \frac{\partial w}{\partial t}+a w\right )$.

%\noindent
%$\displaystyle \frac{\partial^2w}{\partial t\partial x} = \left (\frac{\partial w}{\partial t}+aw\right )\frac{\partial^2w}{\partial x^2}\left ( \frac{\partial w}{\partial x} \right )^{-1} -a \frac{\partial w}{\partial x}+B(x)\left ( \frac{\partial w}{\partial x}+a w\right )$,\hfill\break
%where $a$ is a constant, $B(x)$ is a function. Yurii Kosovtsov
Submitted: 13 Dec 06 11:02
Edited (author): 16 Jan 08 09:37
Edited (admin): 13 Dec 06 12:14
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98 $\displaystyle\frac{\partial^2 w}{\partial x^2}  = (\alpha y + \beta) \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}$. Elena Vyazmina
Submitted: 25 Jan 08 12:42
Edited (admin): 28 Jan 08 16:08
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99 $\displaystyle
\frac{\partial^2 w}{\partial x^2} = \cfrac{\beta}{y}\frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2}$. Elena Vyazmina
Submitted: 25 Jan 08 12:41
Edited (admin): 28 Jan 08 16:16
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100 $\displaystyle
\frac{\partial^2 w}{\partial x^2}=
\left( {\alpha y + \beta } \right)^\gamma \frac{\partial w}{\partial y}\frac{\partial^2 w}{\partial y^2},
\qquad \gamma\ne1$. Elena Vyazmina
Submitted: 25 Jan 08 12:40
Edited (admin): 28 Jan 08 16:20
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Found 106 equations, 11 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 >>

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