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Dependence of entropy solutions in the large for the euler equations on nonlinear flux functions

. We study the dependence of entropy solutions in the large for hyperbolic systems of conservation laws whose flux functions depend on a parameter vector p. We first formulate an effective approach for establishing the L 1 -estimate pointwise in time between entropy solutions for μ ≠ 0 and μ = 0, respectively, with respect to the flux parameter vector p. Then we employ this approach and successfully establish the L 1 -estimate between entropy solutions in the large for several important nonlinear physical systems including the isentropic and relativistic Euler equations and for the isothermal Euler equations, respectively, for which the parameters are the adiabatic exponent y > 1 and the speed of light c < ∞.