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

作者机构：Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA)MIITNanjing 211106China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2023年第43卷第4期

页      面：1668-1674页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：conservation laws p-system vanishing viscosity method BV solutions 

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).Forγ1,the general existence result for large initial data has not been *** 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 *** 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 fixedγ1,either TV(v_(0)(x))or TV(u_(0)(x))can be arbitrarily large.