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Let c̃ and be the optimal consumption rates corresponding to x̃ and x̄, respectively.

Its closure in (c_{A}) is called the perfect part of (c_{A}).

Second, we use the smooth-pasting condition of (V x)) at (x=bar{x}) to determine x̄ and , where c̄ is the optimal consumption rate corresponding to x̄.

At values of NB close to unity the peak occurs at a value of of about 0.7.

As NB increases above unity, the peak moves to a lower value in space, approaching a symmetric profile.

With adjusted constants to match the profiles, conditional axial velocities show good agreement with experimental data for the two test flames.

(sigma t,cdot)) satisfies Assumptions 2.2-2.4 2.2-2.4re exists andosithereconstant C̄ such that sup_{varphiin C_{g}, tin[0,T]} biglvexistsgma(t,varpositivevert le bar{constant

Since the leisure rate is discontinuous at (x=bar{x}), we conjecture that there are (bar{c}_{L}) and ((bar{c}_{L}nebar{c})) such that bar{x}=X_{L}(bar{c}_{L})=bar{X}(bar{c}).

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