文中证明了非线性热传导方程只能有连续解，不可能存在间断解。
In this paper, the author proves that, for a non-linear heat conduction equation, there is no discontinuous solution.
计算结果与已有文献结果基本一致，证明该方法有效、稳定，能够模拟浅水长波方程中的间断解问题。
The numerical results agree with those of available literatures and show that the method is robust and stable for getting the discontinuous solutions of the shallow water wave equation.
即使初始条件十分光滑，双曲守恒律方程的解也可能出现间断。
The solutions of the Hyperbolic conservation laws might develop discontinuity even if the initial conditions are very smooth.
黎曼解涉及的经典基本波包括疏散波、激波和接触间断。
The classical elementary waves in Riemann solutions include rarefaction wave, shock wave and contact discontinuity.
本文采用局部间断有限元方法，给出其数值通量形式并证明了其数值解的存在唯一性。
In this paper, we introduce the numerical flux of the LDG method (local discontinuous Galerkin method) and prove the existence and uniqueness of the LDG numerical solution.
正问题采用间断有限元法求解，反问题的解则在正问题的基础上通过共轭梯度法得到。
The discontinuous finite element method is extended to solve the direct problem, and then the conjugate gradient method is used to solve the inverse problem by optimizing the objective function.
主要分析一维拟线性波方程的解的间断性。
The characteristic method is applied and the weak discontinuous solutions of homogeneous quasilinear wave equations are discussed.
提出了考虑加速度间断特性来改进数值解精度的方法。并作了详尽的讨论。
A method to improve the computational accuracy for numerical solution by considering the acceleration-discontinued characteristics has been given and discussed in detail.
因此很自然的问题就是如何对不同的近似模型的解进行比较，尤其是对带有激波间断的整体弱解进行比较。
Then the natural question is how to estimate the difference of the weak solutions to the systems describing different models, especially to estimate the weak solutions with shock waves.
因此很自然的问题就是如何对不同的近似模型的解进行比较，尤其是对带有激波间断的整体弱解进行比较。
Then the natural question is how to estimate the difference of the weak solutions to the systems describing different models, especially to estimate the weak solutions with shock waves.
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