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- Subjects
- 35-XX Partial differential equations
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We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...
In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.
In this paper, we propose a new numerical method for solving
elliptic equations in unbounded regions of . The
method is based on the mapping of a part of the domain into a
bounded region. An appropriate family of weighted spaces is used
for describing the growth or the decay of functions at large distances. After
exposing the main ideas of the method, we analyse
carefully its convergence. Some 3D computational results are displayed
to demonstrate its efficiency and its high performance.
Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous
cell proliferation and motility rates. The interplay of proliferation and migration
dynamics plays an important role in the invasion of these malignant tumors. We analyze the
regulation of proliferation and migration processes with a lattice-gas cellular automaton
(LGCA). We study and characterize the influence of the migration/proliferation dichotomy
(also known...
Inertial manifold with delay (IMD) for dissipative systems of second order in time is
constructed. This result is applied to the study of different asymptotic properties of
solutions. Using IMD, we construct approximate inertial manifolds containing all the
stationary solutions and give a new characterization of the K-invariant manifold.
The aim of this talk is to present recent results obtained with N. Masmoudi on the free surface Navier-Stokes equations with small viscosity.
We study the convergence in the vanishing viscosity limit of the stationary incompressible Navier-Stokes equation towards the stationary Euler equation, in the presence of an arbitrary force term. This requires that the fluid is allowed to pass through some open part of the boundary.
It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.
We study a microfluidic flow model where the movement of several charged species is coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
We study a microfluidic flow model where the movement of several charged species is
coupled with electric field and the motion of ambient fluid. The main numerical difficulty in this model is the net charge neutrality
assumption which makes the system essentially overdetermined. Hence we propose to use the involutive and the associated augmented form
of the system in numerical computations. Numerical experiments on electrophoresis and stacking show that the completed system significantly improves...
Currently displaying 361 –
380 of
430