We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element met...

We investigate the implications of directional wavefield decomposition with a view to time reversibility. In particular, we discuss how wavefield decomposition preserves the reciprocity theorem of time-convolution type but looses the reciprocity theorem of time-correlation type. As a consequence, a perfect ‘time-reversal mirror’ in the framework of one-way wave theory does not exist: We find th...

A rarefaction wave for system of viscous conservation laws induces strong coupling of waves pertaining to different characteristic fields. For the characteristic field pertaining to the rarefaction wave, there are the nonlinear hyperbolic, linear in time, and the parabolic, sub-linear in time, dissipations. We study the quantitative properties of the waves propagating around the rarefaction wav...

A rarefaction wave for system of viscous conservation laws induces strong coupling of waves pertaining to different characteristic fields. For the characteristic field pertaining to the rarefaction wave, there are the nonlinear hyperbolic, linear in time, and the parabolic, sub-linear in time, dissipations. We study the quantitative properties of the waves propagating around the rarefaction wav...

While GPS is a relatively mature technology, its susceptibility to radio frequency interference (RFI) is substantial. Various investigations, including the Volpe Report (Volpe, 2001) which was the result of a US Presidential Decision Directive (PDD-63) assigned to the Department of Transportation (DOT), have recommended that methods should be developed to monitor, report and locate interference...

An analysis of discretizations of the Helmholtz equation in L 2 and in negative norms (extended version) Flatness of semilinear parabolic PDEs-A generalized Chauchy-Kowalevski approach 27/2012 R. Donninger and B. Schörkhuber Stable blow up dynamics for energy supercritical wave equations 26/2012 P.

In most problems, the ideal situation is having the asymptotic dynamics of one equation the same as the asymptotic dynamics of its discretization. Although, when we are studying the linear wave equation, we note that the spectrum of discretization and the spectrum of its continuous counterpart are far away from each other, no matter how fine the discretization is. This fact is restrictive in th...

In this work, the asymptotic behavior of solutions to a coupled hyperbolic/parabolic{like system is investigated. It is shown that with both components of the equation being subjected to nonlinear damping (boundary damping for the wave component, interior for the beam), a global uniform stability is attained for all (weak) solutions.