One-Dimensional Wave Equations Defined by Fractal Laplacians
We study one-dimensional wave equations deﬁned by a class of fractal Laplacians. These Laplacians are deﬁned by fractal measures generated by iterated function systems with overlaps. We prove the existence and uniqueness of weak solutions. We also study numerical computations of the solutions and prove the convergence of the approximation scheme. This is a joint work with John F. Chan and Alexander Teplyaev.
Fall Eastern Sectional Meeting of the American Mathematical Society (AMS)
Chan, John, Sze-Man Ngai, Alexander Teplyaev.
"One-Dimensional Wave Equations Defined by Fractal Laplacians."
Mathematical Sciences Faculty Presentations.