Stability of stationary solutions of a diffuse interface model for the electrical breakdown process

The aim of the present work is to study qualitative characteristics and to perform a numerical analysis of a diffuse interface model describing the development of an electrical breakdown channel in a solid dielectric. Stability of the system equilibrium positions is analysed. Conditions for the breakdown channel development from small perturbations of the intact medium are found. A differential scheme for the problem is constructed and investigated, an informative estimate of its stability is given. The obtained theoretical results are validated by a computer simulation.