We investigate generalized solutions of nonlinear diffusion equations
and linear hyperbolic equations with discontinuous coefficients in the framework of
Colombeau’s algebra of generalized functions. Under Egorov’s formulation, we obtain
results on existence and uniqueness of generalized solutions, which are shown to be
consistent with classical solutions. The example of a linear hyperbolic equation given
by Hurd and Sattinger [8] has no distributional solutions in Schwartz’s sense, but has
the unique generalized solution. We study what distribution is associated with it,
namely, how it behaves on the level of information of distribution theory.