Abstract
Abstract : This paper discusses the notion of complete stability of mixed initial boundary problems for systems of partial differential equations. The discussion is not restricted to the purely linear case. Moreover, the boundary conditions are permitted to take the form of systems of nonlinear ordinary differential equations. The principal result of the paper is a method for constructing so-called Liapounov functionals by means of which the stability statement is obtained. A second result is a theorem which shows that complete stability follows from the existence of a Liapounov functional. A number of examples are included.
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