Conditions for well-posedness in the Hadamard sense in spaces of generalized functions
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We have used expansions into orthogonal series. In the general case it is natural to use spectral expansions of linear selfadjoint operators. For this one may use the results of [13, 14].
Can the concept of weak well-posedness be carried over to nonlinear problems? Here, probably, J. F. Colombeau's method will turn out to be useful (see [13, 14]).
KeywordsGeneralize Function Nonlinear Problem Selfadjoint Operator Orthogonal Series Spectral Expansion
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