Stability of solutions to hyperbolic systems of conservation laws (Q5948380)

The author studies the Cauchy problem for an \(n\times n\) system of conservation laws in one space dimension: \[ u_t+f(u)_x=0,\qquad u(0,x)=u_0(x). \tag{1} \] Using the method of wave-front tracking the author constructs the piecewise-constant approximating solutions of the problem (1). Is proved the existence of the limits of front-tracking approximates and that these limits determine a unique uniformly Lipschtz continuous semigroup. As a consequence the author obtains the uniqueness and continuous dependence of solutions of the problem (1) on the initial data.