A stability theorem for general quasi-linear symmetric hyperbolic systems (not necessarily conservation laws) is proved in this work. The key assumption is the "stability eigenvalue condition," which requires all the eigenvalues of the constant coefficient system symbol to have negative real part for nonzero Fourier frequency, decaying no faster than omega(2) when omega-->0. The decay of the solution to zero, as time grows to infinity, is proved when the space dimension is bigger than or equal to 3. As an application of the general theorem, stability is proved for the equations describing relativistic dissipative fluids. (C) 2001 American Institute of Physics. [References: 7]
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