Two time-weighted measures are introduced for studying the spatial behavior of the thermoelastic processes in an isotropic thermoelastic body in order to relax the hypotheses of positive definiteness on the thermoelastic coefficients. For the first measure we establish some spatial estimates describing the spatial behavior of solutions for the class of thermoelastic materials for which the Lame´moduli l and m range so that m > 0 and l > À 4 3 m. The second measure allows us to establish spatial

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... estimates describing the spatial behavior of the thermoelastic processes in an isotropic and homogeneous thermoelastic material for which the Lame´moduli range so that m > 0 and À2m < l < 0. Keywords isotropic thermoelastic body, nondefinite elasticity tensor, spatial behavior Several studies on growth and decay spatial behavior for the solutions in the classical linear thermoelastodynamics have appeared in the literature (see, e.g., Boley [1 ], Chirit¸a˘[2-4], Chirit¸a˘and Ciarletta [5, 6], Chirit¸a˘and Da˘nescu [7], Ignaczak [8, 9], Quintanilla [10, 11]). Extensions to other generalized theories of thermoelasticity are also developed (see, e.g., Chirit¸a˘and Scalia [12], Pompei and Scalia [13], Quintanilla [14], Ciarletta and Scalia [15] ). For a thorough review of the field on Saint-Venant's principle and the spatial growth and decay behavior, up to 1996, the reader is referred to the survey articles of Horgan and Knowles [16] and Horgan [17, 18] . The lack of any domain of influence results in the classical linear thermoelasticity has been compensated by a number of spatial decay estimates for the