Bulgariu, Emilian Alternative spatial growth and decay estimates for constrained motion in an elastic cylinder with voids. (English) Zbl 1265.74008 An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 57, No. 2, 341-359 (2011). The author presents a study of the alternative spatial growth and decay behavior for the motion of a finite or semi-infinite cylinder composed of a non-homogeneous anisotropic linear elastic material with voids subject to null supply terms and null lateral boundary conditions. The estimates are derived from a differential inequality depending on the cross-sectional energy flux. An explicit bound, in terms of the problem data, is constructed for the amplitude in each decay estimate. Reviewer: Olivian Simionescu (Bucuresti) Cited in 1 Document MSC: 74B05 Classical linear elasticity 74E20 Granularity 35B45 A priori estimates in context of PDEs Keywords:elastic materials with voids; constrained cylinder; spatial evolution PDFBibTeX XMLCite \textit{E. Bulgariu}, An. Științ. Univ. Al. I. Cuza Iași, Ser. Nouă, Mat. 57, No. 2, 341--359 (2011; Zbl 1265.74008) Full Text: DOI References: [1] Bramble, J. H.; Payne, L. E. - Bounds for solutions of second-order elliptic partial differential equations, Contributions to Differential Equations, 1 (1963), 95-127. · Zbl 0141.09801 [2] Chiriţă, S.; Quintanilla, R. - On Saint-Venant’s principle in linear elastodynamics, J. Elasticity, 42 (1996), 201-215. · Zbl 0891.73010 · doi:10.1007/BF00041790 [3] Cowin, S. C.; Nunziato, J. W. - Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147. · Zbl 0523.73008 · doi:10.1007/BF00041230 [4] Flavin, J. N.; Knops, R. J.; Payne, L. E. - Energy bounds in dynamical problems for a semi-infinite elastic beam, Elasticity: Math. Meth. and Appl, Chichester, 1990, 101-112. · Zbl 0736.73035 [5] Goodman, M. A.; Cowin, S. C. - A continuum theory for granular materials, Arch. Rational Mech. Anal., 44 (1972), 249-266. · Zbl 0243.76005 · doi:10.1007/BF00284326 [6] Ieşan, D. - Thermoelastic Models of Continua, Solid Mechanics and its Applications, 118, Kluwer Academic Publishers Group, Dordrecht, 2004. [7] Knops, R. J.; Payne, L. E. - Alternative spatial growth and decay for constrained motion in an elastic cylinder, Math. Mech. Solids, 10 (2005), 281-310. · Zbl 1074.74009 · doi:10.1177/1081286505036321 [8] Lefter, C.-G. - On a unique continuation property related to the boundary stabilization of magnetohydrodynamic equations, An. Ştiinţ. Univ. ”Al. I. Cuza” Iaşi. Mat. (N. S.), 56 (2010), 1-15. [9] Nunziato, J. W.; Cowin, S. C. - A nonlinear theory of elastic materials with voids, Arch. Rational Mech. Anal., 72 (1979/80), 175-201. · Zbl 0444.73018 · doi:10.1007/BF00249363 [10] Omeike, M. - Stability and boundedness of solutions of some non-autonomous delay differential equation of the third order, An. Ştiinţ. Univ. ”Al. I. Cuza” Iaşi. Mat. (N. S.), 55 (2009), 49-58. · Zbl 1199.34390 [11] Quintanilla, R.; Straughan, B. - Energy bounds for some non-standard problems in thermoelasticity, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 461 (2005), 1147-1162. · Zbl 1145.74337 · doi:10.1098/rspa.2004.1381 [12] Sigillito, V. G. - Explicit a Priori Inequalities with Applications to Boundary Value Problems, Research Notes in Mathematics, 13, Pitman Publishing, London-San Francisco, Calif.-Melbourne, 1977. · Zbl 0352.35002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.