For initial boundary value problems
of linear second order hyperbolic
partial differential equations whose
coefficients depend on countably
many random parameters e.g. via a
Karhunen-Loeve or a wavelet expansion,
we show analyticity of weak solutions
with respect to these parameters.
The problem is reduced to a parametric family of deterministic initial boundary value problems on an infinite dimensional parameter space.
We present convergence rates for polynomial chaos type discretizations as well as for Multi-Level Monte Carlo space-time discretizations.
Seminar for Applied Mathematics
ETH Zurich, CH-8092 Zurich
oint work with
Division of Mathematical Sciences,
School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371