Well-Posedness And Relaxation Limits Of A Hyperbolic-Elliptic Coupled System

In this paper ,we study the initial value problem for a hyperbolic-elliptic coupled system with arbitrary large discontinuous initial data. We study the well-posedness for that model's solutions,then further study two kinds of relaxation limits by means of obtained estimates in front sections,which are hyperbolic-hyperbolic and hyperbolic-parabolic relaxation limits.When we study the well-posedness of solutions,we use the classical vanishing viscosity as our tools. By viscosity approximations equations solutions good properties and strong convergences we may turn to the models initial valure problem. Diss-cussing relaxation limits,we use the classical scaling hyperbolic-type scaling:(x, t) → parabolic-type scaling:...