作者：Lin; Tao; MA; Wei; Yi; SU二维波动方程分形边界分形函数初始速度初始位置计算截面溶液盒维数
摘要：This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The frst case is the equation with classical derivative. The formal solution is obtained. And a defnition of the solution is given. Then we prove that under certain conditions, the solution is a kind of fractal function, which is continuous, diferentiable nowhere in its domain. Next, for specifc given initial position and 3 diferent initial velocities, the graphs of solutions are sketched. By computing the box dimensions of boundaries of cross-sections for solution surfaces, we evaluate the range of box dimension of the vibrating membrane. The second case is the equation with p-type derivative. The corresponding solution is shown and numerical example is given.
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