... 360 The Cauchy characteristic problem Global solvability of the problem Consider the case for f (u) = −λ|u| p u, where λ = and p > are the given real numbers In this case (1.1) takes the form ... to the limit as m → ∞, we obtain (2.4) Thus the lemma is proved Remark 2.5 Before passing to the question on the solvability of the nonlinear problem (2.1), (2.2), we consider this question for ... will, more so, be the strong generalized continuous solution of problem (3.9) There◦ fore, taking into account that G ∈ C(DT ,ST ), by Lemma 3.2, for the function u the integral representation u(x,t)...