A Survey of Hyperbolic Systems of Conservation Laws in Two Dependent Variables

  • J. A. Smoller


This paper is concerned with quasi-linear systems of equations in conservation form of the type
$$u_t + f\left( {u,\upsilon } \right)_x = 0,\,\,\,\,\,\,\,\upsilon _t + g\left( {u,\upsilon } \right)_x = 0,$$
where f and g are smooth functions of two real variables u and v, and u and v are functions of x and t, -∞ < x <∞, t ≥ 0. We assume that the system (1) is hyperbolic, i. e., if we denote by F, the vector function (f,g), then dF(u,v) has real and distinct eigenvalues λ1(u, v) < λ2(u, v), for all values of the argument (u, v) in question. We consider the Cauchy problem for the system (1).


Initial Data Cauchy Problem Existence Theorem Uniqueness Theorem Hyperbolic System 
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© Springer-Verlag Berlin · Heidelberg 1970

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  • J. A. Smoller

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