Regularized symmetric Galerkin BIE formulations in the Laplace transform domain for 2D problems

With reference to some initial-boundary-value problems formulated in the Laplace transform domain, a "regularized" symmetric BIE formulation is derived. The specific problems considered, i.e. diffusion, plane-strain elastodynamics and dynamics of elastic Kirchhoff plates, are formulated in terms of BIEs containing at most weakly (logarithmic) singular kernels. This regularization is achieved by means of the "derivative transfer" technique where, through integration by parts, derivatives are "transferred" from particular auxiliary kernels to the kinematic fields involved in the BIEs.