## ABSTRACT

The prediction of how real world phenomena evolve in time is of the greatest human interest. In order to describe a phenomenon, a mathematical model – called an evolution equation – is constructed, whose solutions are required to reflect the behaviour of that phenomenon. The strategy of qualitative analysis is as follows: the determination of a priori estimates or properties of the solutions to the evolution equation, without solving it explicity. In modelling a real world phenomenon, it is inevitable that the mathematical model obtained will contain many errors. The chapter considers the possible errors made in the measurement of the initial data. A metric space X is locally compact if every closed and bounded subset is compact. The theorem holds: a normed linear space is of finite dimension if and only if every bounded subset is compact.