耗散系统弱解整体存在性

摘要

研究带耗散项的双曲守恒律方程组弱解的整体存在性.对于此类问题,Dafermos和肖玲已经有过具体的研究,但要求非齐次项线性部分为严格对角占优矩阵.本文将条件改为只要求非齐次项对应矩阵的特征值大于零,但要求矩阵为可对角化矩阵.%We address the global existence of weak solutions to hyperbolic system of balance laws with dissipation.The issue has been discussed by Dafermos and Hsiao.However,in their study,the main condition to guarantee the existence of the solution is that the matrix of the linear part of the dissipative terms is a diagonally dominant matrix.In this paper,the condition proposed is that the eigen values of the linear part of the dissipative terms（which is an n × n constant matrix） are all positive,but the matrix is a diagonalizable one.