The transport equations that simulate the passage of the ionic current through an oxide layer under Steady-state conditions have been investigated. These equations are integrated by the method of matched asymptotic expansions. An analysis of the current-voltage characteristic of the system has revealed a region with negative differential conductivity. On this basis, it has been argued that the system is characterized by an instability of the initially uniform distribution of the electric current, which, in turn, leads to the appearance of "current filaments." The threshold value of this instability is determined.
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