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A large class of well posed PDEs is given by [43]
![$\displaystyle {\ddot y} + 2\sum_{k=0}^M q_k \frac{\partial^{2k+1}y}{\partial x^{2k}\partial t} + \sum_{k=0}^N r_k\frac{\partial^{2k}y}{\partial x^{2k}} \protect$](img1666.png) |
(G.30) |
Thus, to the ideal string wave equation Eq. (G.1) we add any number
of even-order partial derivatives in
, plus any number of mixed
odd-order partial derivatives in
and
, where differentiation
with respect to
occurs only once. Because every member of this
class of PDEs is only second-order in time, it is guaranteed to be
well posed, as shown in §L.2.2.
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