Existence Of Solutions Of Cauchy Problem For P-systems With Dissipative Term

This paper studies the existence and periodicity of global weak solutions for p-systems with dissipation term when the initial data is a periodic small perturbations of the initial Riemann data.We use the generalized Glimm format to construct the approximate solution of the equations.However,since the local total variation of the initial value is not small,there will be a second order term when using the traditional construction Glimm functional,which will cause the wave intensity to gradually increase.In order to overcome this difficulty,we first use Riemann invariants to describe the intensity of the wave to prove the local boundedness of the total variation of the approximate solution.Then,combining with the Helly theorem,we can obtain the convergence of the approximate solution sequence.Finally,according to the definition of weak solution,it is proved that the limit of convergence is the weak solution of the original system of equations.In addition,because of the influence of the aperiodic initial data,we prove that the weak solution satisfies periodicity only in some regions of the upper half plane.