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A variational principle for linear evolution problems nonlocal in time. (English. Russian original) Zbl 0835.34078

Sib. Math. J. 34, No. 2, 369-384 (1993); translation from Sib. Mat. Zh. 34, No. 2, 191-207 (1993).
Summary: For a differential operator equation, problems nonlocal in time are considered: a data average in time is prescribed instead of initial data. Solving the problem is reduced to the problem of minimizing a quadratic functional. As an example, the linearized Navier-Stokes system is considered.

MSC:

34G10 Linear differential equations in abstract spaces
49R50 Variational methods for eigenvalues of operators (MSC2000)
35Q30 Navier-Stokes equations
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