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By means of three fundamental structures we can define, in a general way, a sheaf A of differential algebras containing most of the special cases met in the theory of generalized functions.A convenient choice of these structures permits us to study Burgers' equation with δ-Dirac measure as initial data, and we can construct a generalized δ-shock wave as an approximate solution, self-similar to the initial data.
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J.-A. Marti (2003) studied this question.
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