Substantiation of the method of internal averaging along the characteristics of weakly linear systems. II (Q806985)

[For part I see ibid. 29, No.4, 721-732 (1989; Zbl 0711.65081).] The method of internal averaging is generalized to systems having non- uniform integral average. Firstly, the averaging in the class of functions with non-uniform integral average is studied. Then the existence and uniqueness of the solutions of averaged problems are proved. In the last part of the work averaged equations with different classes of initial conditions are investigated. The method described is applicable to a larger class of problems than semi-linear systems of first-order partial differential equations.