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[CT037]

CT037 (1/1) : Parabolic equations and parabolic systems (35K) / Hyperbolic equations and hyperbolic systems (35L)

Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
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
Format : Talk at Waseda University
Author(s) :
- Arnaud Munch (Clermont Auvergne University)

Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
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
Format : Talk at Waseda University
Author(s) :
- Petr Pauš (Czech Technical University in Prague)
- Miroslav Kolář (Czech Technical University in Prague)
- Michal Beneš (Czech Technical University in Prague)

Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
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 Time & Room : 4D (Aug.24, 15:30-17:10) @G602
Type : Contributed Talk
Abstract : We study some inverse problems for hyperbolic conservation laws. Given observations of the entropy solution, we consider the problem of identifying the initial field or the flux function. Due to shockwaves, direct observations of the entropy solution are not "regulated" enough to fit in the Bayesian framework in Stuart (2010). To get round this, we propose a new approach by studying the trajectories for hyperbolic conservation laws and exploring their existence, uniqueness and stability.
Classification : 35L65, 35R30, 62F15, Partial Differential Equations, Inverse Problems
Format : Talk at Waseda University
Author(s) :
- Duc-Lam Duong (LUT University)
- Duc-Lam Duong (LUT University)
- Masoumeh Dashti (University of Sussex)

Session Time & Room : 4D (Aug.24, 15:30-17:10) @G602
Type : Contributed Talk
Abstract : We present Riemann problem governed by $2$-D full Euler system in the Noble-Abel gas. Riemann data, consisting three constants, are distributed in three distinct regions with an assumption that two adjoining regions can be connected by only one planar elementary wave. We present criteria for existence of different configurations of elementary waves for isentropic, as well as full, Euler system. We also discuss the effect of the Noble-Abel gas and the angle of regions on elementary waves and corresponding stream curves. Note: The present article has been published on 17 May 2022 in the journal ''Mathematical Methods in the Applied Sciences''/ Volume 45, Issue 16 with DOI:10.1002/mma.8377.
Classification : 35L65, 35L67, 35Q30, 35Q31, 35Q35, Hyperbolic Conservation Laws, Shocks and Singularities for Hyperbolic equations, Navier-Stokes equations, Euler equations, PDEs in connection with fluid mechanics.
Format : Talk at Waseda University
Author(s) :
- Harsita Srivastava (Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Punjab)
- M. Zafar (Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Punjab)