  We consider the one-dimensional heat and wave equations but -- instead of
boundary conditions-- we impose on the solution certain non-local, integral
constraints. An appropriate Hilbert setting leads to an integration-by-parts
formula in Sobolev spaces of negative order and eventually allows us to use
semigroup theory leading to analytic well-posedness, hence sharpening
regularity results previously obtained by other authors. In doing so we
introduce a parametrization of such integral conditions that includes known
cases but also shows the connection with more usual boundary conditions, like
periodic ones. In the self-adjoint case, we even obtain eigenvalue asymptotics
of so-called Weyl's type.
