Abstract
If Burgers' equation, vt+vvx=δvxx, is used as a descriptor of the propagation of waves of finite amplitude in a viscous fluid, one can give a characterization of the set of boundary functions that are shock-producing. The boundary conditions assumed are v(0,t)=a(t), vx(0,t)=b(t). Conditions for the appearance of shocks are given in terms of the quadratic form a2(t)−2δb(t) by means of the concept of complete monotonicity. The results obtained are an extension of those obtained by the author in “Mathematical Advances in the Theory of One Dimensional Flow,” in Symposium on Apollo Applications, Huntsville, Alabama, January 1966. [Work supported by the National Aeronautics and Space Administration.]
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