Almost periodic solutions and oscillations decay for hyperbolic differential-operator equations

Ya. Yakubov

Abstract


We give an abstract interpretation of such boundary value and initial boundary value problems for hyperbolic differential equations that a part of boundary value conditions may contain also the differentiation on the time t of the same order as equations. The cases of almost periodic solutions and oscillations decay for abstract hyperbolic differential equations are treated. Then we show applications of the obtained abstract results to hyperbolic differential equations. Equations can be, in particular, integra-differential or with a contraction (a stretch) and a shift with respect to the space variable x.

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