On the Mathematical Theory of Deflagrations And Detonations

Cover On the Mathematical Theory of Deflagrations And Detonations
On the Mathematical Theory of Deflagrations And Detonations
Kurt Otto Friedrichs
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Fur- ther we see that the term representing the kinetic energy has dropped out from (2).
Tlie boundary conditions are 9 = ©, £ = 1 at x = od, and £=Oatx=-oo. The constant Q Is given by Q = E. +9, . The relation ^^ + 9^ = Q, which holds for regular solutions deter- mines the value 9 = 9 atx = -oo. O To investigate possible solutions of this problem one may consider 9 as Independent variable running from 9 to 9, and combine the equations to (^) dL 2A S(9) 1 - £ ^'^ ^ ^-^E, . 9, -E^^^9) -9 It is i
...mmediately seen that this equation has a saddle-sliagularity at the point 9 = 9^, £ = 1. There is just one solution curve that enters this point from the region £ ©3 provided p A/m^ is sufficiently large; If p A/m^ is sufficiently small the curve will enter the line 9=9 at a point with E > 0, It is thus clear that there is just one value of p A/m^ for which the curve enters the line 9=9 with £ = 0.

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