Eigenfunction expansions in thermoelasticity

AbstractWe develop spectral theorems for a certain class of (non-) selfadjoint differential operators via eigenfunction expansions. To this end at first the equations of linear thermoelasticity are dealt with in the whole space for an isotropic, homogeneous medium. By means of Fourier transformation we obtain an eigenfunction expansion for the non-selfadjoint operator acting on the space-variables yielding also a representation of the solution of the time-dependent problem which allows a description of the asymptotic behaviour (time t → ∞). Then the results are generalized for a class of operators satisfying certain conditions on their spectra