Existence and uniqueness of an energetic solution is proved to an initial-boundary value problem for a semilinear
divergence-form hyperbolic differential equation. Specifically, the case is considered when on the one lateral surface
of a cylinder there is given a third nonuniform boundary condition whereas on the other one there is a uniform Dirichlet
boundary condition. We also prove the existence and uniqueness of an energetic solution to the problem for a
linear divergence-form hyperbolic equation with a Radon measure on the right hand side of the equation.
|
