Two-dimensional wave equations with fractal boundaries

摘要

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.