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[CT037]

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : The modeling and mathematical analysis of concrete phenomena are of great interest to better understand our environment and its evolution. Several analogies between chemistry and biological systems have led researchers to introduce mathematical models of "reaction-diffusion", whose objective is to follow the evolution of the quantities interacting during the process. In this talk, we are interested in reaction-diffusion systems with exponential growth, modeling an irreversible chemical reaction. Since the 86's, considerable efforts have been devoted to the study of this systems. We provide a general overview of the different theoretical results obtained, as well as our investigation from a numerical point of view on open cases.
Classification : 35K57, 35K58, 80A25, 80A19
Author(s) :
- Rajae Malek (Moulay Ismail University, Meknes, Morocco)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : Our contribution deals with the phenomenon in material science called multiple cross-slip of dislocations in slip planes. The numerical model is based on a mean curvature flow equation with additional forcing terms included. The curve motion in 3D space is treated using our tilting method, i.e., mapping of a 3D situation onto a single plane where the curve motion is computed. The physical forces acting on a dislocation curve are evaluated in the 3D setting.
Classification : 35K57, 35K65, 65N40, 65M08, 53C80
Author(s) :
- Petr Pauš (Czech Technical University in Prague)
- Miroslav Kolář (Czech Technical University in Prague)
- Michal Beneš (Czech Technical University in Prague)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : Paper aims is to design boundary control for the considered fractional reaction-diffusion system with delays by proving the wellposedness of kernel function using backstepping method. An invertible Volterra integral transformation is used to find an appropriate stable target system. Different from existing ones, the results are discussed using Lyapunov-Krasovskii theory and sufficient conditions are derived with the help of LMI approach. Finally, proposed conditions are numerically validated over time fractional-order reaction-diffusion cellular neural network model.
Classification : 35K58, 35K57, 93D05, 93D15
Author(s) :
- Mathiyalagan Kalidass (Bharathiar University, Coimbatore)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : We addresses the controllability of the semi-linear heat equation $\partial_t y- \partial_{xx} y+f(y)=0$, $x\in (0,1)$. Assuming that the function $f$ is $C^1$ over $\mathbb{R}$ and $\limsup_{\vert r\vert\to \infty} \vert f^\prime(r)\vert/\ln^{3/2}\vert r\vert\leq \beta$ for some $\beta>0$ small enough, we show that a fixed point application related to a linearized equation is contracting yielding a constructive method to approximate boundary controls for the semi-linear equation. Similar ideas are used to address the controllability for semi-linear wave type equations.
Classification : 35K58, 93B05
Author(s) :
- Arnaud Munch (Clermont Auvergne University)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : We consider the fourth-order total variation flow equation in $\mathbb{R}^n$. We characterize the solution in terms of what is called the Cahn-Hoffman vector field, and introduce a notion of calibrability of a set in our fourth-order setting. This notion is related to whether a characteristic function preserves its form throughout the evolution. If $n \neq 2$, all annuli are calibrable. In the case $n = 2$, if an annulus is too thick, it is not calibrable.
Classification : 35K67, 35K25, 47J35
Author(s) :
- Hirotoshi Kuroda (Hokkaido University)
- Yoshikazu Giga (The University of Tokyo)
- Michał Łasica (Polish Academy of Sciences)