An Asymptotic Analysis of An Expanding Detonation

Cover An Asymptotic Analysis of An Expanding Detonation
An Asymptotic Analysis of An Expanding Detonation
James Jones
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The linear part of (5. 4) at (±v^, 0)is A = V (0 -a.
±v.
There is a double zero eigenvalue at the origin, and only one eigenspace (the V axis). This is a double zero bifurcation point, about which more will be said later. When v = v^ (resp. -v^), there is one zero eigenvalue, with the v axis as corresponding eigenspace, and one positive (resp. Negative) eigen- value with a corresponding unstable (resp. Stable) separatrix solution. These are simple zero bifurcation points which vanish for k posi
...tive. The v axis is the common center manifold for the bifurcation points.
If the factor of X is removed from the vector field (5. 4) the resulting modified vector field has the same phase curves as the original field except along X = 0. This modified field has no critical points and thus possesses a continuous structurally stable flow. The phase flow of (5. 4) thus consists of -30 a line of critical points superimposed over a continuous one parameter family of phase curves. Setting k = in (5.


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