论文标题
奇异地形的海啸传播
Tsunami propagation for singular topographies
论文作者
论文摘要
我们考虑具有奇异系数的海啸波方程，并证明其具有非常弱的溶液。此外，我们在某种意义上显示了非常弱的解决方案的独特结果和一致性定理。在一维病例中，对正规化问题的家族进行了数值实验。特别是，观察到大量第二波的出现，从奇异性点/线沿相反的方向传播。它的结构和强度进行数值分析。此外，对于二维海啸方程，我们开发了GPU计算算法以降低计算成本。
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the very weak solution with the classical one in some appropriate sense. Numerical experiments are done for the families of regularised problems in one- and two-dimensional cases. In particular, the appearance of a substantial second wave is observed, travelling in the opposite direction from the point/line of singularity. Its structure and strength are analysed numerically. In addition, for the two-dimensional tsunami wave equation, we develop GPU computing algorithms to reduce the computational cost.
