A new approach to ill-posed evolution equations : C-regularized and B- bounded semigroups.
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Date
2001
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Abstract
The theory of semigroups of linear operators forms an integral part of Functional
Analysis with substantial applications to many fields of the natural sciences. In
this study we are concerned with the application to equations of mathematical
physics. The theory of semigroups of bounded linear operators is closely related to
the solvability of evolution equations in Banach spaces that model time dependent
processes in nature.
Well-posed evolution problems give rise to a semigroup of bounded linear operators.
However, in many important and interesting cases the problem is ill-posed
making it inaccessible to the classical semigroup theory. One way of dealing
with this problem is to generalize the theory of semigroups.
In this thesis we give an outline of the theory of two such generalizations, namely,
C-regularized semigroups and B-bounded semigroups, with the inter-relations
between them and show a number of applications to ill-posed problems.
Description
Thesis (Ph.D.)-University of Natal, Durban, 2001.
Keywords
Evolution equations., Semigroups of operators., Linear operators., Theses--Mathematics.