Far Eastern Mathematical Journal

To content of the issue


The solvability of the boundary value problem for the system of thermoelasticity equations in space


Sulyandziga E.P.

2017, issue 1, P. 98-109


Abstract
The proposed and substantiated boundary value problem for the linearized three-dimensional system of thermoelasticity equations describing the deformation of a solid body because of its temperature. The existence of weak solutions was proved.

Keywords:
setting the boundary value problem, system of thermoelasticity, the existence of solutions, estimation of approximate solutions, thermal expansion

Download the article (PDF-file)

References

[1] A.D. Kovalenko, Termouprugost', Izdatel'skoe ob"edinenie “Vishcha shkola”, Kiev, 1975.
[2] P.V. Bazylev, A.V. Izotov, A.I. Kondrat'ev, V.A. Lugovoi, K.N. Okishev, “Gosudarstvennyi pervichnyi etalon edinits skorostei rasprostraneniia prodol'nykh, sdvigovykh i poverkhnostnykh ul'trazvukovykh voln v tverdykh sredakh GET 1989-2012.” , Izmeritel'naia tekhnika, 7:7, (2013), 6–10.
[3] A.P. Filin, Prikladnaia mekhanika tverdogo deformiruemogo tela: soprotivlenie materialov s elementami teorii sploshnykh sred i stroitel'noi mekhaniki, Nauka, M., 1978.
[4] V. Novatskii, Dinamicheskie zadachi termouprugosti, Mir, M., 1970.
[5] A.A. Samarskii, P.N. Vabishchevich, Vychislitel'naia teploperedacha, Editorial URSS, M., 2003.
[6] E.P. Suliandziga, “O kraevykh zadachakh dlia odnomernoi sistemy uravnenii termouprugosti”, Vestnik TOGU, 3(34), (2014), 29–38.
[7] Y. Sun, D. Fang, M. Saka and A.K. Soh, “Laser-Induced Vibrations of Micro-Beams under Different Boundery Conditions”, International Journal of Solids and Structures, 45:7–8, (2008), 1993–2013.
[8] H.M. Youssef, A.S. Al-Felali, “Generalized Thermoelasticity Problem of Material Subjected to Thermal Loading Due to Laser Pulse”, Applied Mathematics, 3, (2012), 142–146.
[9] Zh.-L. Lions, Nekotorye metody resheniia nelineinykh kraevykh zadach, Mir, M., 1972.
[10] O.A. Ladyzhenskaia, Matematicheskie voprosy dinamiki viazkoi neszhimaemoi zhidkosti, Nauka, M., 1970.

To content of the issue