Abstract
Abstract A mathematical model of an arms race is presented in which the armaments are classified according to their quality. Necessary and sufficient conditions are obtained for the existence of equilibrium weapon stocks and their asymptotic stability in the case of a race with updating and renewal of certain strategic weapon stocks. A concept of balance of power is introduced and preconditions needed for such a balance of power are discussed. The analysis basically leads to an investigation of a coupled linear system of parabolic equations with non-local feedback boundary conditions. This type of boundary value problem appears to be new to the literature on partial differential equations especially boundary value problems.
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