# Solve Hamilton–Jacobi PDE

$$\begin{cases} \frac{\partial S}{\partial t} + \frac{1}{2}\left((\nabla S)^2 + (x, \Omega^2 x) \right)= 0 \\ S|_{t=0} = (k,x) \end{cases}$$ Where $x \in \mathbf{R}^n,\ \Omega^2$ - Positive-definite matrix, $k$ is constant vector

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Maybe you could add more context, for example tell us what $k$ is (constant or a function). –  Davide Giraudo Dec 27 '11 at 16:51
@Davide k is constant vector –  Philipp G. Sinicyn Dec 27 '11 at 18:45
How is $\partial S/\partial x$ a scalar? Is it supposed to be understood as $\nabla S\cdot x$? –  anon Dec 27 '11 at 18:53
@anon corrected –  Philipp G. Sinicyn Dec 27 '11 at 21:00