On quasilinear generalized canonical hyperbolic systems of first-order partial differential equations (Q1810246)

This paper deals with systems of equations in \(\mathbb{R}^{m+1}\) \((m\geq 1)\) of the form \[ {\partial u_i(x,t)\over\partial t}+ \sum^m_{j=1} \lambda_{ij}(x, t) {\partial u_i(x,t)\over\partial x_j}= f_i(x,t,u(x, t)),\tag{1} \] \(i= 1,\dots, n\), where \(n\geq 1\), \(x= (x_1,\dots, x_m)\), \(u= (u_1,\dots, u_n)\). Using the method of characteristics, the author proves theorem on continuous solvability and studies properties of solutions of the mixed Cauchy boundary value problem for (1).