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Volume 1,     Number 2,     Spring 1993

 

AN EXACT SHOCK SOLUTION
G.R. NICKLASON AND M. HEGGIE

Abstract. A nonlinear, second order differential equation arising from the integro-differential equation 1 - f2(α) = (d/dα) ∫_α V(α-β)f(β)dβ for the relaxation function V(α) = A1e-α/λ1 +A2e-α/λ2 is solved for certain values of the input parameters {A1, A2, λ1, λ2}. The solution is seen to depend upon a class of functions known as generalized binomial functions. These functions satisfy a particular type of functional equation and their occurrence, while not previously noted in this context, may be rather widespread. It is observed that the solution of the corresponding first order problem arising from the choice V(α) = Ae-α/λ also depends upon a particular generalized binomial function.

 

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