A Stability Estimate for a Solution to the Wave Equation with the Cauchy Data on a Timelike Cylindrical Surface

We consider the linear wave equation in a domain of the x, t-space bounded from above and below by some smooth surfaces and from the sides by a cylindrical surface with generator parallel to the t-axis. We study the Cauchy problem for this equation with data on a piece of the timelike cylindrical surface and establish a stability estimate for a solution to the problem.