On spatial growth or decay of solutions to a non simple heat conduction problem in a semi-infinite strip

The present paper establishes growth and decay spatial properties for the solutions of a fourth–order initial boundary value problem describing the flow of heat in a non–simple heat conductor along a semi–infinite strip in R2. The method of time–weighted line and area integral measures is used. When the time–weighted line integral measure is used, then an alternative of Phragmén–Lindelof type is established. It is shown that the decay rate of the end effects is controlled by the same factor as in the steady–state case (governed by the biharmonic equation), that is exp (-(√2 π)/h x1), where h is the width of the strip and x1 is the distance to the end of the strip. When an appropriate combination of the time–weighted line and area integrals is used as a measure, then a decay estimate of Saint–Venant type is established and it is shown that the end effects decay more rapidly as do their counterparts in the steady–state case.