INITIAL-BOUNDARY VALUE-PROBLEMS IN LINEAR VISCOELASTICITY ON THE HALF-SPACE

After deriving the linear hereditary constitutive laws for viscoelasti city, deducing frequency representation and the correspondence princip le to linear elastodynamics the weak form of the equations of motion a nd their decomposition into pseudo-wave equations are stated. Applying a Laplace transform in the time domain the Green's tensor is construc ted by means of a spatial distributional Fourier transform. A detailed discussion of the four main initial-boundary value problems with pres cribed displacement and traction components on the plane {x(3) = 0} le ads to half-space representations by inverse Fourier integrals. Finall y some asymptotic behaviour of the solution in the original time domai n is deduced.