We show that the wave map equation in ${\bf R}^{1+1}$ is in general ill posed in the critical space $\dot{H}^{1/2}$, and the Besov space $\dot{B}_{2}^{1/2,1}$. The ...

Solving the one-dimensional wave equation is an undergraduate problem. We consider problems of time-harmonic waves interacting with N scatterers: they could be beads on a long string, for example. If ...

Previously it has been shown that all finite energy, causal solutions of the time-dependent three-dimensional acoustic equation and Maxwell's equations have forms for large radius that, except for a ...