Two-dimensional wave equations with fractal boundaries

Abstract

Wave equations are one of the three types of classical partial differential equations of second order. These equations arise in mathematical modelling of the motion of vibrating strings and membranes, and are typical in studying partial differential equations of second order. Wave equations in the sense of classical derivative with smooth boundaries have been investigated extensively. However, few studies on membranes with fractal boundaries have appeared in the literature. This article is devoted to two types of two-dimensional wave equations with fractal boundaries.

Keywords:

• wave equations
• classical derivative
• p-type derivatives
• fractal boundary

AMS Subjects Classifications:

• 35G15
• 28A80

Acknowledgement

This work was supported by the National Natural Science Foundation of China (Grant No. 10571084).