{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:06:16Z","timestamp":1787321176489,"version":"build-2736575974"},"reference-count":35,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2005,1]]},"abstract":"<jats:p>This note addresses the mathematical study of a nonlinear model arising in the description of the macroscopic thermomechanical behavior of shape memory materials and previously introduced in [R. Peyroux, A. Chrysochoos, Ch. Licht, and M. L\u00f6bel, J. Phys. C4 Suppl., 6 (1996), pp. 347--356]. In particular, we discuss the model derivation and investigate a system of PDEs coupled with a vectorial variational inequality. We develop the analysis in both the dissipative and the nondissipative cases, providing indeed a quantitative asymptotic connection between the two regimes. Moreover, we prove the global in time well-posedness for suitable initial and boundary value problems. As a by-product of the well-posedness analysis, we address a variable time-step discretization procedure, proving indeed its convergence and providing some a priori error bounds. Finally, we deal with the asymptotic behavior of the system for large times and establish the convergence of the trajectories to the solution of a suitable stationary problem.<\/jats:p>","DOI":"10.1137\/s0036141004444251","type":"journal-article","created":{"date-parts":[[2005,9,7]],"date-time":"2005-09-07T21:00:16Z","timestamp":1126126816000},"page":"130-155","source":"Crossref","is-referenced-by-count":5,"title":["Analysis of a Thermomechanical Model for Shape Memory Alloys"],"prefix":"10.1137","volume":"37","author":[{"given":"Ulisse","family":"Stefanelli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","first-page":"163","volume":"12","author":"Achenbach M.","year":"1982","journal-title":"J. Phys. C4 Suppl."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"S. Antman, J. L. Ericksen, D. Kinderlehrer, and I. 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