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Classical solution of the Cauchy problem for a quasi-linear wave equation with discontinuous initial conditions

“…the Fourier method [6], such as increased requirements for smoothness of functions and matching of functions, i. e., functions must satisfy some additional matching and smoothness conditions, it has allowed us to consider a large number of problems of dynamic impact theory, see [7][8][9][10] and cited literature. Also, we note the classical d'Alembert method (the method of characteristics), which is not as powerful as functional methods.…”

“…The initial-value problem ( 1), ( 2) has a unique classical solution in the sense of Definition. This solution is determined by formulas (3), (6), and (8).…”