Affiliations: Department of Intelligent Mechanical Engineering, Faculty of Engineering, Fukuoka Institute of Technology, Fukuoka, Japan. E-mail: h-takeda@fit.ac.jp | Department of Engineering for Production and Environment, Graduate School of Science and Engineering, Ehime University, Ehime, Japan. E-mail: yoshikawa@ehime-u.ac.jp
Note: [] Corresponding author: Shuji Yoshikawa, Department of Engineering for Production and Environment, Graduate School of Science and Engineering, Ehime University, 3 Bunkyo-cho, Matsuyama, Ehime, 790-8577 Japan. Tel.: +81 89 927 9719; Fax: +81 89 927 9744; E-mail: yoshikawa@ehime-u.ac.jp
Abstract: The aim of this paper is to investigate asymptotic behavior of solutions to the Cauchy problem of certain fourth-order semilinear elastic system with weak damping in three space dimension. The system corresponds to the isothermal case of the thermoelastic system representing the martensitic phase transitions on shape memory alloys. We give several asymptotic profiles of solutions. By considering the second-order expansion of solutions, we obtain more precise information about asymptotic behavior of solutions as t→∞, and observe the contribution of the nonlinear term to solutions. Moreover, we give the third-order expansion formula which enable us to clarify the relation between the fourth- and the second-order derivative term.
Keywords: asymptotic profile, shape memory alloy, initial value problem, semilinear elastic system, higher-order expansion of solution
