期刊文献+
共找到1篇文章
< 1 >
每页显示 20 50 100
Two-dimensional Wave Equations with Fractal Boundaries 被引量:1
1
作者 Lin Tao MA Wei Yi SU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第12期2321-2342,共22页
This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The first case is the equation with classical derivative. The formal solution is obtained. And a definition of the solution is... This paper focuses on two cases of two-dimensional wave equations with fractal boundaries. The first case is the equation with classical derivative. The formal solution is obtained. And a definition of the solution is given. Then we prove that under certain conditions, the solution is a kind of fractal function, which is continuous, differentiable nowhere in its domain. Next, for specific given initial position and 3 different 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. 展开更多
关键词 von koch type curve p-type derivative two-dimensional wave equation fractal boundary fractal dimension
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部