Christiaan C. Stolk

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In certain applications one is interested in the long-time behavior of systems described by a linear partial differential equation. For example, in kinetic equations one studies the decay to equilibrium of various linear and nonlinear systems. For the Kramers–Fokker–Planck equation, which will be studied here, exponential decay was shown in Talay (1999) and(More)
A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the(More)
In this paper we use methods from partial differential equations, in particular microlocal analysis and theory of Fourier integral operators, to study seismic imaging in the wave-equation approach. Seismic data are commonly modeled by a high-frequency single scattering approximation. This amounts to a linearization in the medium coefficient about a smooth(More)
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations respresent parametrically the spatially varying mechanical(More)
A nonlinear singularity-preserving solution to seismic image recovery with sparseness and continuity constraints is proposed. We observe that curvelets, as a directional frame expansion, lead to sparsity of seismic images and exhibit invariance under the normal operator of the linearized imaging problem. Based on this observation we derive a method for(More)