Jin-Xin模型初边值问题整体光滑解的存在性

Existence of Global Smooth Solution to Initial Boundary Value Problem for Jin-Xin Model

运用特征线法和一阶拟线性双曲系统极大值原理 ,在松弛时间ε充分小的条件下 ,对初值不做任何小性假设 ,得到解的先验估计 ,证明了 Jin- Xin模型初边值问题整体光滑解的存在性 .

Applying the method of characteristic and the maximum principle of first-order quasilinear hyperbolic system, under the assumption that the relaxation time ε is sufficiently small, we obtain some a priori estimates of the solution and prove the existence of the global smooth solution to the initial boundary value problem for the Jin-Xin model without any smallness assumption for the initial data.