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Nonlocal in time problems for evolution equations of second order

Avalishvili G. A.

Journal of Applied Analysis

2002

Vol. 8, nr 2

245-259

In this paper, nonlocal in time problem for abstract evolution equation of second order is studied and theorem on existence and uniqueness of its solution is proved. Some applications of this theorem for hyperbolic partial differential equations and systems are considered and it is proved, that well-posedness of the mentioned problems depends on algebraic properties of ratios between the dimensions of the spatial boundary and the times appearing in the nonlocal in time initial conditions.