458 research outputs found
A stable imaging functional for anisotropic periodic media in electromagnetic inverse scattering
The paper is concerned with the inverse scattering problem for Maxwell's
equations in three dimensional anisotropic periodic media. We study a new
imaging functional for fast and stable reconstruction of the shape of
anisotropic periodic scatterers from boundary measurements of the scattered
field for a number of incident fields. This imaging functional is simple to
implement and very robust against noise in the data. Its implementation is
non-iterative, computationally cheap, and does not involve solving any
ill-posed problems. The resolution and stability analysis of the imaging
functional is investigated. Our numerical study shows that this imaging
functional is more stable than that of the factorization method and more
efficient than that of the orthogonality sampling method in reconstructing
periodic scatterers.Comment: 23 page
Existence and Decay of Solutions of a Nonlinear Viscoelastic Problem with a Mixed Nonhomogeneous Condition
We study the initial-boundary value problem for a nonlinear wave equation
given by u_{tt}-u_{xx}+\int_{0}^{t}k(t-s)u_{xx}(s)ds+ u_{t}^{q-2}u_{t}=f(x,t,u)
, 0 < x < 1, 0 < t < T, u_{x}(0,t)=u(0,t), u_{x}(1,t)+\eta u(1,t)=g(t),
u(x,0)=\^u_{0}(x), u_{t}(x,0)={\^u}_{1}(x), where \eta \geq 0, q\geq 2 are
given constants {\^u}_{0}, {\^u}_{1}, g, k, f are given functions. In part I
under a certain local Lipschitzian condition on f, a global existence and
uniqueness theorem is proved. The proof is based on the paper [10] associated
to a contraction mapping theorem and standard arguments of density. In Part} 2,
under more restrictive conditions it is proved that the solution u(t) and its
derivative u_{x}(t) decay exponentially to 0 as t tends to infinity.Comment: 26 page
Large time behavior of differential equations with drifted periodic coefficients modeling Carbon storage in soil
This paper is concerned with the linear ODE in the form
, which represents a simplified
storage model of the carbon in the soil. In the first part, we show that, for a
periodic function , a linear drift in the coefficient involves
a linear drift for the solution of this ODE. In the second part, we extend the
previous results to a classical heat non-homogeneous equation. The connection
with an analytic semi-group associated to the ODE equation is considered in the
third part. Numerical examples are given.Comment: 18 page
The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions
This paper is concerned with the existence and the regularity of global
solutions to the linear wave equation associated with two-point type boundary
conditions. We also investigate the decay properties of the global solutions to
this problem by the construction of a suitable Lyapunov functional.Comment: 18 page
Existence, blow-up and exponential decay estimates for a nonlinear wave equation with boundary conditions of two-point type
This paper is devoted to study a nonlinear wave equation with boundary
conditions of two-point type. First, we state two local existence theorems and
under suitable conditions, we prove that any weak solutions with negative
initial energy will blow up in finite time. Next, we give a sufficient
condition to guarantee the global existence and exponential decay of weak
solutions. Finally, we present numerical resultsComment: 2
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