ABSTRACT
Time dependent equations occur frequently in mathematical physics with perhaps the most common examples being the linear wave equation and the linear heat equation. When studying the initial value problems and initial boundary value problems associated with such equations the first requirement is to declare what type of solution to such problems is being sought. For example, are the solutions expected to be classical solutions in the sense that they posses the appropriate number of continuous derivatives or are they expected to be more generalised types of solution? Once existence and uniqueness results have been obtained for the required type of solution attempts can then be made to obtain other details of the solutions such as their regularity and their asymptotic behaviour.
