Singular And Nonuniform Limits of Solutions of the Boltzmann Equation

Harold Grad

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The two types of existence theorems are quite distinct. For example, u = can be imposed on the entire boundary of D, but conservation of mass implies u^ = at one end (or at infinity) if it holds at the opposite end of a one- dimensional problem. Also, suitable regularity and boundedness conditions at infinity are needed for the unbounded domain.
The basic boundary condition involves specifying the half distribution function f~, ^ • n

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