The Existence Of Global Weak Solutions Of The P-systems With Disspation

In this paper, we study the periodic solutions of the p ? systems with dissipation term. In order to prove the existence of the weak solutions, we present a periodic version of the Glimm scheme. The p ? systems are the Larange coordinate of the one-dimensional isentroptic ideal fluid dynamics equations. The Glimm scheme is an important method to study the hyperbolic conservation equations of the weak solutions, which is proposed by Glimm in 1965. In 1968, Nishida first discovered the p- systems for adiabatic case which proved the existence of solutions of initial value problem and solved the general initial value problem for the simplest of the gas dynamics equations. Bakhvalov and DiPerna extended the theorem and got more positive results. On the basis of their research, Frid studied the conservation equations of conservation law of initial value. we obtain the existence of Global Weak Solutions. In this paper, we study the periodic solutions of the p ? systems with dissipation term for the global existence of weak solutions. To construct the approximate solutions of the equations, we use the generalized Glimm scheme. We obtain the approximate solutions which are bounded and variations boundedness by using Riemann problems as framework and join the nonhomogeneous term information. What’s more, we get that there exists a convergent subsequence in the BV-space, and the limit of the subsequence is the weak solution of the equations.