Renata Bunoiu

Existence Theorem for a Nonlinear Elliptic Shell Model

In this paper we introduce a new nonlinear shell model with the following properties. First, we show that, if the middle surface of the undeformed shell is elliptic, then this new nonlinear shell model possesses solutions which are also elliptic surfaces. Second, we show that, if in addition the middle surface of the undeformed shell is a portion of a sphere, then the total energy of this nonlinear shell model coincides to within the first order, i.e., for “small enough” change of metric and change of curvature tensors, with the total energy of the well-known Koiter nonlinear shell model.

Bingham flow in porous media with obstacles of different size

By using the unfolding operators for periodic homogenization, we give a general compactness result for a class of functions defined on bounded domains presenting perforations of two different size. Then we apply this result to the homogenization of the flow of a Bingham fluid in a porous medium with solid obstacles of different size. Next, we give the interpretation of the limit problem in terms of a nonlinear Darcy law. Copyright

Vectorial approach to coupled nonlinear Schrödinger systems under nonlocal Cauchy conditions

The paper presents a vectorial approach for coupled general nonlinear Schrödinger systems with nonlocal Cauchy conditions. Based on fixed-point principles, the use of matrices with spectral radius less than one, and on basic properties of the Schrödinger solution operator, several existence results are obtained. The essential role of the support of the nonlocal Cauchy condition is emphasized and fully exploited.

Unfolding homogenization in doubly periodic media and applications

We define a reiterated unfolding operator for a doubly periodic domain presenting two periodicity scales. Then we show how to apply it to the homogenization of both linear and nonlinear problems. The main novelty is that this method allows the use of test functions with one scale of periodicity only and it considerably simplifies the proofs of the convergence results. We illustrate this new approach on a Poisson problem with Dirichlet boundary conditions and on the flow of a power law fluid in a doubly periodic porous medium.