No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 24 October 2008
In his paper on ‘The propagation of weak spherical shocks in stars’ Whitham(1) uses as the basis of his non-linear theory the solution of the linear equation
where the suffixes denote partial derivatives and A, B, C are functions of r only. In obtaining his solution he assumes (i) that
where ξ = t – ∫dr/A and fn(ξ) is the nth integral of f with respect to ξ, and (ii) that the function f may be identified with the corresponding function which occurs when gravity is neglected, i.e. when A becomes the constant A0, B = −2/r and C = 0. Having assumed that (2) exists, Whitham is able to show that it will hold asymptotically for Aξ/r ≪ 1 and A′ = O (A/r).