AUTHORS: Michael Gil

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ABSTRACT: Let H be a Hilbert space with the unit operator I. We consider linear non-autonomous distributed parameter systems governed by the equation dy/dt = S(t)y + B(t)y (y = y(t), t > 0), where S(t) is an unbounded operator, such that for some constant c, S(t)+cI is dissipative; B(t) is an operator uniformly bounded on [0, ∞), having a uniformly bounded derivative and commuting with S(t). Exponential stability conditions are established. An illustrative example is presented.

KEYWORDS: distributed parameter system, linear nonautonomous system, stability

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