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I am wondering if there is a general way of splitting the following PDE into two separate equations. I would like to re-write the second-order spatial derivatives on the LHS as first-order derivatives.

[tex]

\[

\frac{{\partial p^2 }}{{\partial x^2 }} + \frac{{\partial p^2 }}{{\partial y^2 }} = A\frac{{\partial ^2 p}}{{\partial t^2 }} + B\frac{{\partial p}}{{\partial t}}

\]

[/tex]

So once the above equation is split, there should be two equations involving only first-order spatial derivatives ([tex]\partial p/\partial x[/tex] and [tex]\partial p/\partial y[/tex]).

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# Splitting PDE into system of PDEs

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