On Blow–up Solutions of Initial Characteristic Problem for Nonlinear Hyperbolic Systems with Two Independent Variables
نویسندگان
چکیده
Global solvability of the problem (1),(2) was studied rather thoroughly (see, e.g., [1– 9] and the literature quoted therein). In the present paper new sufficient conditions of existence and nonexistence of so called blow-up solutions to the problem (1),(2) are given. To formulate the main results, we need to introduce the following notation and definitions. z = (zi) n i=1 ∈ R n is a vector with components z1, . . . , zn, and ‖z‖ is its Euclidean norm. v ·w is the scalar product of the vectors v and w ∈ Rn. Ω0(a1, b1) = {(x, y) : 0 ≤ x < a1, 0 ≤ y ≤ b} ∪ {(x, y) : 0 ≤ x ≤ a, 0 ≤ y < b1} . Ω0(a1, b1) is the closure of the set Ω0(a1 , b1), i.e., Ω0(a1 , b1) = (
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