On string vibrations influenced by a smooth obstacle at one of the endpoints

In this paper, the vibrations of a string are considered. At one end of the string, a smooth obstacle is placed and the other end of the string is attached to a fixed point. The contact between the string and the obstacle varies in time, and leads to a linear, moving boundary value problem for the string vibrations. By applying a boundary...

On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that...