ON SINGULAR CHARACTERISTIC INITIAL VALUE PROBLEMS WITH UNIQUE SOLUTIONS

Abstract : A special class of characteristic first-order initial value problems are considered. The initial value problem arises in the asymptotic solution of parabolic and elliptic equations. The problem is characterized by a singular, characteristic initial manifold. Namely, initial data is given on a characteristic curve. The characteristic curve is also singular in that there is a point on the initial manifold where the equation = 0. That such problems have unique solutions is proven. The theorem also has an interesting interpretation in terms of the calculus of variations.

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