Journal of Applied Analysis 08 (2002), No. 2, 245--259
Copyright Heldermann Verlag 2002
Nonlocal in Time Problems for Evolution Equations of Second Order
Gia A. Avalishvili
Institute of Applied Mathematics, Tbilisi State University, University Str. 2, 380043 Tbilisi, Georgia
We study a nonlocal-in-time problem for abstract evolution equations of second order and prove a theorem on the existence and uniqueness of its solution. Some applications of this theorem for hyperbolic partial differential equations and systems are considered and it is proved that the well-posedness of the problems depends on algebraic properties of the ratios between the dimensions of the spatial boundary and the times appearing in the nonlocal-in-time initial conditions.
Keywords: Second-order evolution equation, nonlocal in time conditions, algebraic numbers.
MSC: 11J68, 35L55; 35L90
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