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In this paper we investigate the spatial behavior of the solutions for
a theory for the heat conduction with one delay term. We obtain a Phragm én-
Lindelöf type alternative. That is, the solutions either decay in an exponential
way or blow-up at in nity in an exponential way. We also show how to obtain
an upper bound for the amplitude term. Later we point out how to extend
the results to a thermoelastic problem. We nish the paper by considering
the equation obtained by the Taylor approximation to the delay term. A
Phragm én-Lindelöf type alternative is obtained for the forward and backward
in time equations.
CitationLeseduarte, M.C.; Quintanilla, R. Phragmén-Lindelöf alternative for an exact heat conduction equation with delay. "Communications on pure and applied analysis", 01 Maig 2013, vol. 12, núm. 3, p. 1221-1235.
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