| Contents |
| I will discuss some integrodifferential equations of which the simplest is
\[
u _ { t t } + \mu u = J \star u
\]
where $J \in L ^ 1 ( \mathbf R ^ { 1 + n })$ is nonnegative and $\mu = \int J$.
This equation is very far from satisfying Huygens' principle. In fact,
the support of any nonzero solution is all of $\mathbf R ^ { 1 + n }$.
It can, nonetheless, be thought of as an analogue of the wave equation
and satisfies some of the same estimates. It even exhibits a sort of
``almost finite speed of propagation.'' |
|