If one considers a superconducting half-space, i.e superconducting for x>0, and weak external magnetic field B0 applied along z direction in the empty space x<0, then inside the superconductor the magnetic field is given by
In a superconducting region with x>0, where an external magnetic field B0 is present along the z-axis in the region x<0, the magnetic field within the superconductor is described as