A penalization method for a suitable reformulation of the governing equations as a constrained optimization problem provides accurate numerical simulations for large-amplitude travelling water waves in irrotational flows and in flows with constant vorticity.
In this paper, a perturbation theory for the nonlinear Schrödinger equation with non-vanishing boundary conditions based on the inverse scattering transform is presented. It is applied to study the stability of the soliton propagation on a continuous-wave background. It is shown that the soliton is rather robust with respect to dispersive perturbations but it can be strongly affected by damping. In particular, it is shown that adiabatic approaches can underestimate the decay of the soliton energy.
In this paper, we derive time reversal imaging functionals for two strongly causal acoustic attenuation models, which have been proposed recently. The time reversal techniques are based on recently proposed ideas of Ammari et al. for the thermo-viscous wave equation. Here and there, an asymptotic analysis provides reconstruction functionals from first order corrections for the attenuating effect. In addition, we present a novel approach for higher order corrections. Copyright
The narrow escape problem consists of deriving the asymptotic expansion of the solution of a drift-diffusion equation with the Dirichlet boundary condition on a small absorbing part of the boundary and the Neumann boundary condition on the remaining reflecting boundaries. Using layer potential techniques, we rigorously find high-order asymptotic expansions of such solutions. We explicitly show the nonlinear interaction of many small absorbing targets. Based on the asymptotic theory for eigenvalue problems developed in [2], we also construct high-order asymptotic formulas for eigenvalues of the Laplace and the drifted Laplace operators for mixed boundary conditions on large and small pieces of the boundary.Mathematics Subject Classification (MSC2000): 35B40, 92B05
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