奇异地形的海啸传播
Tsunami propagation for singular topographies
摘要：
考虑一类具有奇异系数的海啸波方程，证明了它有一个很弱解。在适当的意义下，我们还证明了非常弱解与经典解的唯一性和相容性。数值实验在一维和二维情况下的正规化问题的家庭。特别地，观察到实质性的第二波的出现，其从奇点/线沿相反方向行进。并对其结构和强度进行了数值分析。此外，对于二维海啸波动方程，我们开发了GPU计算算法，以降低计算成本。
英文摘要：
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.
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