Existence in the Large for Pressure-Gradient System

摘要

In this paper,the authors use Glimm scheme to study the global existence of BV solutions to Cauchy problem of the pressure-gradient system with large initial data.To this end,some important properties of the shock curves of the pressure-gradient system in the Riemann invariant coordinate system and verify that the shock curves satisfy Diperna’s conditions(see[Diperna,R.J.,Existence in the large for quasilinear hyperbolic conservation laws,Arch.Ration.Mech.Anal.,52(3),1973,244–257])are studied.Then they construct the approximate solution sequence through Glimm scheme.By establishing accurate local interaction estimates,they prove the boundedness of the approximate solution sequence and its total variation.