(untitled) (Journal of Partial Differential Equations, 2020)
In this paper the initial-boundary-value problems for pseudo-hyperbolic system of quasi-linear equations: (-1)^Mu_tt + A(x, t, U, V)u_x^2M_tt = B(x, t, U, V)u_x^2M_t + C(x, t, U, V)u_x^2M + f(x, t, U, V) u_x^k(0,t) = &#968_0k(t), u_x^k(l,t) = &#968_lk(t), k = 0,1,&#8230,M - 1 -u(x,0) = &#966_0(x), u_t(x,0) = &#966_1(x) is studied, where U = (u_1, u_x,&#8230,u_x^2M - 1) V = (u_t, u_xt,&#8230,u_x^2M - 1_t), A, B, C are m &#215 m matrices, u, f, &#968_0k, &#968_1k, &#968_0, &#968_1 are m-dimensional vector functions. The existence and uniqueness of the generalized solution (in H&sup2 (0, T; H^2M (0, 1))) of the problems are proved.