We consider second order hyperbolic equations with unbounded
operator's coefficients possessing time dependent domain of
definition in a Hilbert space. Existence and uniqueness of the
strong generalized solution are studied. The proofs rely on a
generalization of the well known energy integral method. First, we
derive a priori estimates for the strong generalized solutions with
the help of Yosida operator approximation. Then, using previous
results, we show that the range of the operators generated by the
posed problem is dense.
Primary Subjects: 35B45
Secondary Subjects: 35D05, 35L90, 35L10, 35L20
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