  The two-dimensional transient problem that is studied concerns a
semi-infinite crack in an isotropic solid comprising an infinite strip and a
half-plane joined together and having the same elastic constants. The crack
propagates along the interface at constant speed subject to time-independent
loading. By means of the Laplace and Fourier transforms the problem is
formulated as a vector Riemann-Hilbert problem. When the distance from the
crack to the boundary grows to infinity the problem admits a closed-form
solution. In the general case, a method of partial matrix factorization is
proposed. In addition to factorizing some scalar functions it requires solving
a certain system of integral equations whose numerical solution is computed by
the collocation method. The stress intensity factors and the associated weight
functions are derived. Numerical results for the weight functions are reported
and the boundary effects are discussed. The weight functions are employed to
describe propagation of a semi-infinite crack beneath the half-plane boundary
at piecewise constant speed.
