Uniqueness and Stability Theorem for the Generalized Solution of the Initial-Value Problem for a Class of Quasi-Linear Equations in Several Space Variables

in the region t>0. Here x =(Xl, x2 . . . . , xn), u =u(t, x), the f j , j = 1, 2, . . . , n, are continuously differentiable functions of a single real variable, and u0 (x) is in the class F; i.e., Uo(X) is a bounded function having locally bounded variation in the sense of TOt~LLI-CESARI. Moreover for each fixed t, u(t, x) is in the same class F. A… (More)