  In this article, we consider the one-dimensional stochastic wave and heat
equations driven by a linear multiplicative Gaussian noise which is white in
time and behaves in space like a fractional Brownian motion with Hurst index
$H\in (\frac 14,1)$. We prove that the solution of each of the above equations
is continuous in terms of the index $H$, with respect to the convergence in law
in the space of continuous functions. The proof is based on a tightness
criterion on the plane and Malliavin calculus techniques in order to identify
the limit law.
