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This work is part of a general study on the long-term safety of thegeological repository of nuclear wastes. A diffusion equation with a movingboundary in one dimension is introduced and studied. The model describes somemechanisms involved in corrosion processes at the surface of carbon steelcanisters in contact with a claystone formation. The main objective of thepaper is to prove the existence of global weak solutions to the problem. Forthis, a semi-discrete in time minimizing movements scheme \`a la De Giorgi isintroduced. First, the existence of solutions to the scheme is established andthen, using a priori estimates, it is proved that as the time step goes to zerothese solutions converge up to extraction towards a weak solution to the freeboundary model.

Analysis of a one dimensional energy dissipating free boundary model with nonlinear boundary conditions. Existence of global weak solutions