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[CT038]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Geometric flows are geometric evolution equations often depicting physical phenomena. We consider a class of geometric flows of order $2m \in 2\mathbb{N}$ describing evolving $n$-manifolds attached to fixed hypersurfaces with some nonlinear boundary conditions. We modify the theory of Maximal Regularity to accommodate quasilinear parabolic PDEs with such boundary conditions. For initial conditions in $W_p^{2m – \frac{2m}{p}}, p\geq \max\{2m, \frac{n}{2m}\}$) we show well-posedness and instantaneous smoothing of the solution on a maximal interval of existence.
Classification : 35Kxx, 35Qxx
Author(s) :
- Daniel Goldberg (Technion-Israel Institute of Technology)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Work in passive tracers investigates how properties of a tracer distribution depend on boundary conditions and properties of the underlying fluid flow. We apply shape optimization to discover extremal domains for Poiseuille flow informed by analytic predictions of spatial moments - such as mean, effective diffusivity, skewness - derived in prior work. With this combination of asymptotic formulas and numerical study, we find and report on surprising nonlinear behavior depending on shape parameters.
Classification : 35Kxx, 90C90
Author(s) :
- Manuchehr Aminian (California State Polytechnic University Pomona)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The talk will give an up-to-date result on singularity formation in the Keller-Segel system in $\mathbb{R}^d$. For $d \geq 2$, there exist blowup solutions that are of Type II with finite mass. Blowup rates are completely quantized. There also exist Type I blowup solutions with infinite mass for $d = 3, 4$. The constructed solution is asymptotically self-similar with a logarithmic correction to its profile which is either radial or non-radial.
Classification : 35M10, 35K40, 35K55, 35K57
Author(s) :
- Van Tien Nguyen (National Taiwan University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We propose a DDFV for a coupled nonlinear parabolic-elliptic equations. The system is known as a generalization of the Thermistor problem which models a temperature dependent electrical resistor. We first establish some a prior estimates satisfied by the sequences of approximate solutions. Then, it yields the compactness of these sequences. Passing to the limit in the numerical scheme, we finally obtain that the limit of the sequence of approximate solutions is a weak solution to the problem under study.
Classification : 35M30, 35K92, 35J46, 65N08
Author(s) :
- Manar Lahrache (Moulay Ismail University, Faculty of Science, Meknes, Morocco)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We consider a system of equations describing a spherically symmetric $n$-dimensional motion of a gaseous star, whose gas is viscous, heat-conducting, self-gravitating and bounded by the free-surface, and flows around a central rigid sphere. We discuss first unique existence of the solution to the corresponding stationary problem, and next do a large-time behaviour of the flow, under a certain restricted but physically plausible condition on parameters and initial data.
Classification : 35M33, 35Q30, 35R35, 35Q85, 76N10
Author(s) :
- Morimichi Umehara (University of Miyazaki)