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»ã±¨ÌáÒª£ºConsider the Cauchy problem for a multidimensional first-order quasilinear hyperbolic system with a relaxation term of and a parameter standing often for the relaxation time. This kind of systems include a large number of physical models such as the Euler equations with damping, the Euler-Maxwell system for plasma and the M1-model in the radiative transfer theory etc. We are interested in the relaxation limit of the system as the relaxation time tends to zero. I will describe the formal derivation of parabolic equations from the system in a slow time scaling. Under stability conditions, the justification of the limit is shown for smooth solutions, locally in a uniform time interval and globally in time when initial data are close to constant equilibrium states.

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