# Registered Data

Contents

- 1 [CT033]
- 1.1 [00132] Incompatibility-governed deformations: a new approach to Elastoplasticity
- 1.2 [00102] Existence of Sign-changing solutions to a Hamiltonian elliptic System
- 1.3 [00228] Density functional theory for two dimensional homogeneous materials
- 1.4 [01203] Existence and regularity results for nonlinear elliptic equations with degenerate coercivity
- 1.5 [02424] Nonlinear fractional elliptic systems : Theory and Numerics

# [CT033]

## [00132] Incompatibility-governed deformations: a new approach to Elastoplasticity

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We present theoretical as well as numerical results concerning a novel approach to model elasto-plastic phenomena in deformable solids based on a decomposition of the total deformation tensor into a compatible (i.e., a symmetric gradient) and an incompatible part at each point of the domain. The incompatible part aims to model the part of the deformation due to dislocation movement that eventually is responsible for the creation of plastic regions. This is a joint work with Samuel Amstutz (Ecole Polytechnique de Palaiseau, France).**Classification**:__35J48__,__49S05__,__74C05__,__74G99__,__80A17__**Author(s)**:**Nicolas Van Goethem**(Universidade de Lisboa )

## [00102] Existence of Sign-changing solutions to a Hamiltonian elliptic System

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We consider the Hamiltonian elliptic system \begin{equation*} - \Delta U + U= |V|^{p-1}V \quad\text{ and } \quad - \Delta V + V=|U|^{q-1}U \,\text{ in } \mathbb{R}^N, \end{equation*} where $N\geq 4$ and the non-linearities $p,q$ are superlinear and satisfy sub-critical hyperbola condition. We prove the existence of nonradial sign-changing solutions. We shall work with the space of $\phi$-equivariant functions where $\phi:\Gamma\to \{1,-1\}$ and $\Gamma\subset O(N)$, a closed subgroup of $O(N)$.**Classification**:__35J50__**Author(s)**:**Alok Kumar Sahoo**(Ph.D. student, IIT Hyderabad)- Bhakti Bhusan Manna (IIT Hyderabad)

## [00228] Density functional theory for two dimensional homogeneous materials

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: We study Density Functional Theory models for 2D materials. We first show that a homogeneous material can be seen as a limit of crystals. Next, we derive reduced models in the orthogonal direction. We show how the different terms of the energy are modified and prove some properties of the ground state. In Kohn-Sham models, we prove that the Pauli principle is replaced by a penalization term in the energy.**Classification**:__35J50__,__47J30__,__47N50__,__Mathematical physics__**Author(s)**:**Salma Lahbabi**(UHIIC, UM6P)- David Gontier (Université Paris Dauphine)
- Salma Maichine (UM6P)
- Abdelqoddous Moussa (UM6P)

## [01203] Existence and regularity results for nonlinear elliptic equations with degenerate coercivity

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: In this research we drive the existence and regularity results for solutions of some nonlinear degenerate Dirichlet problems containing two lower order terms, the fi rst is a nonlinear convection term satisfying an optimal growth conditions and without any hypothesis of coercivity and the second is a zero order perturbation term, which called the hardy potential, that creates an obstruction to the existence of a solution. Not also that for right hand side, it is assumed that to be an L^m-function with m⩾1.**Classification**:__35J60__,__35K65__,__35J70__**Author(s)**:**Fessel Achhoud**(MISI Laboratory Hassan First University of Settat)- Abdelkader Bouajaja (MISI Laboratory Hassan First University of Settat)

## [02424] Nonlinear fractional elliptic systems : Theory and Numerics

**Session Date & Time**: 5B (Aug.25, 10:40-12:20)**Type**: Contributed Talk**Abstract**: In this talk, we focus on a class of elliptic systems with gradient source terms, governed by the fractional Laplacian $(-\Delta)^s$ of order $0**Classification**:__35J66__,__35K57__,__65N30__,__35-00__,__65-00__**Author(s)**:**Maha Daoud**(Hassan II University of Casablanca)