The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main part ...

Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite differe...

We detail the spectrum of the linearized Vlasov-Poisson equation, and construct an original integro-differential operator which is related to the eigenstructure. It gives a new representation formula for the electric field, and yields new estimates for the linear Landau damping. Then we apply the technique to a problem with a dependence to the Debye length, and show weaker damping for small Deb...

We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of a linearized Bäcklund transformation whose domain has codimension one. Combining a linear stability result with a general theory of nonlinear stability by Friesecke and Pego for solitary waves in lattice equations, we conclude that all solitons in the Toda lattice are asymptotically stable in an exp...

We study the numerical recovery of Manning’s roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the co...

In this work, we study the existence ofC local solutions to 2-Hessian equation in R . We consider the case that the right hand side function f possibly vanishes, changes the sign, is positively or negatively defined. We also give the convexities of solutions which are related with the annulation or the sign of right-hand side function f . The associated linearized operator are uniformly elliptic.

The mean operator R0 and its dual R0 play an important role and have many applications, for example, in image processing of the so-called synthetic aperture radar (SAR) data [11, 12] or in the linearized inverse scattering problem in acoustics [6]. Our purpose in this work is to define and study integral transforms which generalize the operators R0 and R0. More precisely, we consider the follow...

This paper reviews Fréchet sensitivity analysis for partial differential equations with variations in distributed parameters. The Fréchet derivative provides a linear map between parametric variations and the linearized response of the solution. We propose a methodology based on representations of the Fréchet derivative operator to find those variations that lead to the largest changes to the s...

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...

This paper is devoted to the well-posedness of the stationary 3d Stokes-Coriolis system set in a half-space with rough bottom and Dirichlet data which does not decrease at space infinity. Our system is a linearized version of the Ekman boundary layer system. We look for a solution of infinite energy in a space of Sobolev regularity. Following an idea of Gérard-Varet and Masmoudi, the general st...