Conditions for well-posedness in the Hadamard sense in spaces of generalized functions

Abstract

We make some remarks in connection with the results of Secs. 6–10. 1. 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]. 2. 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]).