THE GLOBAL EXISTENCE OF BV SOLUTIONS OF THE ISENTROPIC p-SYSTEM WITH LARGE INITIAL DATA  

作　　者：吴菲 王泽军 陈芳启 Fei WU;Zejun WANG;Fangqi CHEN(Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China;Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106,China)

机构地区：[1]Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China [2]Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106,China

出　　处：《Acta Mathematica Scientia》2023年第4期1668-1674,共7页数学物理学报（B辑英文版）

基　　金：partially the NSFC(11671193);Fangqi Chen was partially the NSFC(12172166,11872201)。

摘　　要：In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av^(-γ).Forγ>1,the general existence result for large initial data has not been obtained.By using the Glimm scheme,Nishida,Smoller and Diperna successively obtained the global existence results for(γ-1)TV(v_(0)(x),u_(0)(x))being small.In the present paper,by adopting a rescaling technique,we improve these results and obtain the global existence result under the condition that(γ-1)^(γ+1)(TV(v_(0)(x)))~(γ-1)(TV(u_(0)(x)))^(2) is small,which implies that,for fixedγ>1,either TV(v_(0)(x))or TV(u_(0)(x))can be arbitrarily large.

关 键 词：conservation laws P-SYSTEM vanishing viscosity method BV solutions 

分 类 号：O175[理学—数学]