带耗散项等温的p-方程组大初值解的整体存在性

Global Existence of Large Initial Value Solutions for Isothermal p-Equations with Dissipative Term

研究带耗散项的等温情形的p-方程组大初值解的存在性.对于此类问题我们主要是应用改进的Glimm格式来证明解的存在性.C.M.Dafermous和L.Hsiao曾对一般的带耗散的守恒律做出了相关的研究,但主要适用于小初值的情形.该文中通过对于Riemann问题和波强度进行详细的分析,得到了在L∞∩BV(R)空间中弱解的整体存在性.

Abstract：The existence of large initial value solutions for isothermal p-equations with dissipa- tive term is studied. For such a problem, we are mainly using the improved Glimm scheme to prove the existence of the solution. C. M. Dafermous and L. Hsiao had made relevant research on the general conservation laws with dissipation, but it is mainly suitable for the case of small initial value. In this paper, through a detailed analysis for the Riemann problem and the wave intensity, we get the global existence of weak solutions in space L^∞ ∩ BV（R）.