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List of Equations

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

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3. Linear Partial Differential Equations

3.6. Systems of Equations

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1 \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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