磁流体力学方程组一维活塞问题激波解的整体存在性

Global existence of shock front solution to one-dimensional piston problem of magnetogasdynamics equations

研究磁流体力学方程组一维活塞问题,证明了当活塞速度是一个常数的扰动时,其激波解的整体存在性.通过改进的Glimm格式先构造问题的近似解,然后对基本波的相互作用作出精确的估计,最后构造Glimm泛函并证明其单调性.

In this paper, we consider the global existence of shock front solu- tion to one-dimensional piston problem of magnetogasdynamics equations when the velocity of the piston is a small perturbation of constant. We first use an improved Glimm scheme to construct the approximate solution of this problem. Then, we establish precise estimates to the interactions of elementary waves. At last, we construct the Glimm functional and prove the monotonicity of the Glimm functional.