ABSTRACT
Chapter 3
Regularization Methods
In the rst two chapters we investigated the Cauchy problem
u
(t) = Au(t); t 0; u(0) = x; (CP)
where A : D(A) X ! X , which is not uniformly well-posed. The
technique of integrated and C-regularized semigroups presented in Chapter
1 allows one to construct a solution of (LCP) for initial values x from
various subsets of D(A) stable in X with respect to x in corresponding
graph-norms. The technique of distributions presented in Chapter 2 allows
the construction of a generalized solution for any x 2 X stable in a space
of distributions.
