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Stability of solutions to hyperbolic systems of conservation laws. (English. Russian original) Zbl 1026.35074
J. Math. Sci., New York 104, No. 2, 933-940 (2001); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat Obz. 66, 5-15 (1999).
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.

35L65 Hyperbolic conservation laws
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