  We investigate the Loschmidt echo, the overlap of the initial and final
wavefunctions of Luttinger liquids after a spatially inhomogeneous interaction
quench. In studying the Luttinger model, we obtain an analytic solution of the
bosonic Bogoliubov-de Gennes equations after quenching the interactions within
a finite spatial region. As opposed to the power law temporal decay following a
potential quench, the interaction quench in the Luttinger model leads to a
finite, hardly time dependent overlap, therefore no orthogonality catastrophe
occurs. The steady state value of the Loschmidt echo after a sudden
inhomogeneous quench is the square of the respective adiabatic overlaps. Our
results are checked and validated numerically on the XXZ Heisenberg chain.
