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List of Equations

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

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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>
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71 3. Linear Partial Differential Equations
3.5. Higher-Order Equations
$\displaystyle ax^b \frac{\partial ^2w}{\partial t^2}+\frac{\partial^3w}{\partial x^3}=0$. Valeriy Stepuchev
Submitted: 13 May 08 20:01
Edited (author): 07 Oct 15 17:20
Edited (admin): 10 Jun 08 11:44
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72 3. Linear Partial Differential Equations
3.5. Higher-Order Equations
$\displaystyle \frac{\partial ^2w}{\partial t^2}+at^b\frac{\partial^mw}{\partial x^m}=0$,\hfill\break
where $b\neq-2;\ b\neq-2\pm\frac 1k; \ k=1,2,3,...$ Valeriy Stepuchev
Submitted: 09 Sep 10 18:56
Edited (author): 08 Oct 15 18:29
Edited (admin): 01 Sep 13 12:42
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73 3. Linear Partial Differential Equations
3.5. Higher-Order Equations
$\displaystyle \frac{\partial ^3w}{\partial t^3}+
at^b\frac{\partial^mw}{\partial x^m}=0$,\hfill\break
where $b\neq-3; \ b\neq-3\pm\frac 1k; \ b\neq-3\pm\frac 2k; \ k=1,2,3,...$ Valeriy Stepuchev
Submitted: 14 Sep 10 19:37
Edited (author): 08 Oct 15 18:44
Edited (admin): 01 Sep 13 12:49
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74 3. Linear Partial Differential Equations
3.6. Systems of Equations
\noindent
$\displaystyle \frac{\partial w_i}{\partial t}=\sum_{j=1}^n {\Large L}_{i,j}(t,\vec{x})\cdot w_j+\phi_i(t,\vec{x}),\qquad i=1,\dots,n$,\hfill\break
where $t$ and $\vec{x}=(x_1,\dots,x_m)$ are independent variables, $w_i=w_i(t,\vec{x})$ are dependent variables, 
${\Large L}_{i,j}(t,\vec{x})$ are arbitrary \emph{linear differential operators}, 
which do not depend on $\frac{\partial}{\partial t}$, and $\phi_i(t,\vec{x})$ are arbitrary functions.

%\noindent
%$\displaystyle \frac{\partial}{\partial t}w_i(t,\vec{x})=\sum_{j=1}^n {\Large \hat{D}}_{i,j}(t,\vec{x})\cdot w_j(t,\vec{x})+\phi_i(t,\vec{x})\qquad (i=1,\dots,n)$,\hfill\break
%where $t$ and $\vec{x}=(x_1,\dots,x_m)$ are independent variables, ${\Large \hat{D}}_{i,j}(t,\vec{x})$ are arbitrary \emph{linear differential operators}, which do not depend on $\frac{\partial}{\partial t}$ explicitely, $\phi_i(t,\vec{x})$ are arbitrary functions. Yurii Kosovtsov
Submitted: 12 Dec 06 09:50
Edited (author): 15 Dec 06 11:08
Edited (admin): 13 Dec 06 12:19
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75 4. Nonlinear Partial Differential Equations
4.1. Second-Order Quasilinear Parabolic Equations
\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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76 4. Nonlinear Partial Differential Equations
4.1. Second-Order Quasilinear Parabolic Equations
\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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77 4. Nonlinear Partial Differential Equations
4.1. Second-Order Quasilinear Parabolic Equations
$\displaystyle \frac{\partial {w}}{\partial t} = a\frac{\partial}{\partial
x}\left(w^m\frac{\partial {w}}{\partial x}\right)+bw^{1-m}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:07
Edited (admin): 23 Mar 07 10:27
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78 4. Nonlinear Partial Differential Equations
4.1. Second-Order Quasilinear Parabolic Equations
$\displaystyle \frac{\partial {w}}{\partial t} = a\frac{\partial}{\partial
x}\left(e^{\lambda w}\frac{\partial {w}}{\partial x}\right) +
b\,e^{-\lambda w}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:01
Edited (admin): 23 Mar 07 10:42
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79 4. Nonlinear Partial Differential Equations
4.1. Second-Order Quasilinear Parabolic Equations
$\displaystyle \frac{\partial {w}}{\partial t} = \frac{\partial}{\partial
x}\left(w^{m}\frac{\partial {w}}{\partial x}\right) +
aw-bw^{1+m}+ cw^{1-m}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:19
Edited (admin): 23 Mar 07 11:04
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80 4. Nonlinear Partial Differential Equations
4.1. Second-Order Quasilinear Parabolic Equations
$\displaystyle \frac{\partial w}{\partial t} =
\frac{1}{r^n}\frac{\partial}{\partial
r}\left(r^n ae^{\lambda w}\frac{\partial w}{\partial r}\right) +
b\,e^{-\lambda w}$. Elena Andreevna Vyazmina
Submitted: 21 Dec 06 13:29
Edited (admin): 23 Mar 07 11:06
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Found 327 equations, 33 pages (10 eqs. per page): << 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 >>

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