Weak solutions of the Cauchy problem for the second-order hyperbolic differential-operator equation with a variable domain
New theorems of existence, uniqueness and continuous dependence of weak solutions of the Cauchy problem for the second-order hyperbolic differential-operator equation with a variable domain of a smooth unbounded operator coefficient are proved. A new method to prove the uniqueness of weak solutions of hyperbolic differential-operator equations is suggested. Correct solvability in the weak sense of the mixed problem for the wave equation with the time-dependent boundary condition is established.