An initial-boundary value problem for bending of a piecewise homogeneous thermoelastic plate with transverse shear deformation is studied, and its unique solvability in spaces of distributions is proved by means of a combination of the Laplace transformation and variational methods.
Constanda, C.A Mathematical Analysis of Bending of Plates with Transverse Shear Deformation , Longman/Wiley, Harlow-New York, 1990.
2.
Schiavone, P. and Tait, R.J.Thermal effects in Mindlin-type plates. Quarterly Journal of Mechanics and Applied Mathematics, 46, 27-39 ( 1993).
3.
Kupradze, V.D. , Gegelia, T.G., Basheleishvili , M.O. and Burchuladze, T.V.Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam, 1979.
4.
Chudinovich, I. and Constanda, C.The transmission problem in bending of plates with transverse shear deformation. IMA Journal of Applied Mathematics, 66, 215-229 (2001).
5.
Chudinovich, I. and Constanda, C.Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation, Chapman and Hall/CRC Press, London-Boca Raton, FL, 2000.
6.
Chudinovich, I. and Constanda, C.Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes, Springer, London, 2005.
7.
Chudinovich, I., Constanda, C. and Colín Venegas, J.The Cauchy problem in the theory of thermoelastic plates with transverse shear deformation. Journal of Integral Equations and Applications, 16, 321-342 ( 2004).
8.
Lions, J.-L. and Magenes, E.Non-homogeneous Boundary Value Problems and Applications, Vol. 1. Springer, Berlin, 1972.
9.
Mizohata, S.The Theory of Partial Differential Equations, Cambridge University Press, Cambridge, 1973 .