The question of the continuous dependence of solutions to an optimal control problem on data (the so-called stability analysis of solutions or well-posedness) is very important from the point of view of practical applications of theory. Indeed, if the problem is related to a physical phenomenon, its data can be considered only an arbitrarily close approximation to exact values. Consequently, if...

Abstract We study the plane-symmetric collision of two gravitational waves and describe global spacetime geometry generated by this collision. formulate characteristic initial value problem for Einstein equations, when Goursat data describing incoming are prescribed on null hypersurfaces. construct a solution representing cyclic based junction conditions associated with singularity scattering m...