Impulse Trajectory and Final Controllability of Parabolic-Hyperbolic Systems*

The authors analyze the existence and uniqueness of the generalized solutions to boundary-value problems for equations of parabolic-hyperbolic type with generalized functions of finite order in their right-hand sides. The motivation is the analysis of the problems of trajectory and final controllability of systems described by these boundary-value problems and subjected to concentrated influences of impulse or point type. The systems can be considered “toy models” of the interaction of a solid body and a liquid. A priori inequalities in negative norms are obtained. The theorems of the existence and uniqueness of the generalized solutions and theorems of the trajectory and final controllability of systems with singular influences are proved.