TY - JOUR

T1 - Almost periodic solutions and oscillations decay for hyperbolic differential-operator equations

AU - Yakubov, Ya.

N1 - Functional differential equations and applications (Beer-Sheva, 2002)

PY - 2003

Y1 - 2003

N2 - We study boundary value and initial boundary value problems for abstract second-order hyperbolic differential-operator equations in which the boundary conditions may depend on the second-order time derivative of the solution. The cases of almost periodic solutions and oscillations decay for these abstract hyperbolic differential equations are treated. Applications of the abstract results obtained to hyperbolic differential equations are given. In particular, the equations considered can be integro-differential or contain a contraction (or expansion) and a shift with respect to the space variable x. In the case of oscillations decay we show that the solution u(t,x) of the corresponding initial boundary value problem tends to zero weakly in W22(0,1) and u′t(t,x) tends to zero weakly in W12(0,1) as t→∞.''

AB - We study boundary value and initial boundary value problems for abstract second-order hyperbolic differential-operator equations in which the boundary conditions may depend on the second-order time derivative of the solution. The cases of almost periodic solutions and oscillations decay for these abstract hyperbolic differential equations are treated. Applications of the abstract results obtained to hyperbolic differential equations are given. In particular, the equations considered can be integro-differential or contain a contraction (or expansion) and a shift with respect to the space variable x. In the case of oscillations decay we show that the solution u(t,x) of the corresponding initial boundary value problem tends to zero weakly in W22(0,1) and u′t(t,x) tends to zero weakly in W12(0,1) as t→∞.''

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SN - 0793-1786

VL - 10

SP - 315

EP - 330

JO - Functional Differential Equations

JF - Functional Differential Equations

IS - 1-2

ER -