M. Grigolia

Some Remarks on The Initial Problems for Nonlinear Hyperbolic Systems

abstract:
For a nonlinear hyperbolic system with two independent variables a priori estimates of solutions of a general initial problem are established. On the basis of these estimates sufficient conditions for the solvability and well-posedness of this problem are found.

Mathematics Subject Classification: 35L15, 35L70

Key words and phrases: Nonlinear hyperbolic system, initial problem, characteristic problem, Goursat problem, Darboux problem, Cauchy problem, a priori estimate, solvability, well-posedness.