Periodic BV Solutions Of P-System With Dissipative Source

The main work of this paper is to study the periodic solution of a system of equations with partial dissipative terms,and prove the existence and large-time behavior of the weak solution of the system of equations.This paper first obtains the existence of weak solutions of the equations based on the random choice method and the operator splitting method,and gives the equations based on Dafermos research Partial dissipative conditions of the system and the specific form of the kawashima condition,then the large-time behavior of the solution to the system of dissipative terms equations is proved according to the energy method proposed in [5],we find that the dissipation conditions of this system of equations are similar to the properties of positive semi-definite matrices,and by example,the conditions required for the results of this paper are better than strong dissipative conditions(i.e.,strictly diagonally dominant matrices).Finally,combined with the random point method,a local solution of the equation can be constructed with a small initial value,and the total change of the local solution is known from [7] The poor exponential decay is determined by the strong diagonally dominant nature of a matrix,so we transform the original system so that the matrix corresponding to the transformed new system meets this property,and then the exponential decay of the BV solution of the system is obtained.