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In this paper we study the spatial behaviour of solutions for the three-phase-lag heat equation
on a semi-infinite cylinder. The theory of three-phase-lag heat conduction leads to a
hyperbolic partial differential equation with a fourth-order derivative with respect to time.
First, we investigate the spatial evolution of solutions of an initial boundary-value problem
with zero boundary conditions on the lateral surface of the cylinder. Under a boundedness
restriction on the initial data, an energy estimate is obtained. An upper bound for the
amplitude term in this estimate in terms of the initial and boundary data is also established.
For the case of zero initial conditions, a more explicit estimate is obtained which
shows that solutions decay exponentially along certain spatial–time lines. A class of
non-standard problems is also considered for which the temperature and its first two time
derivatives at a fixed time T0 are assumed proportional to their initial values. These results
are relevant in the context of the Saint–Venant Principle for heat conduction problems.
CitationQuintanilla, R. Spatial behavior of solutions of the three-phase-lag heat equation. "Applied mathematics and computation", Juliol 2009, vol. 213, núm. 1, p. 153-162.
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