# Registered Data

Contents

- 1 [CT038]
- 1.1 [02692] Discovering extremal domains via shape optimization for passive tracers
- 1.2 [02566] A spherically symmetric and steady flow describing the motion of a viscous gaseous star
- 1.3 [02581] Well-Posedness and smoothness of geometric flows with nonlinear boundary conditions
- 1.4 [01080] About Thermistor Problem: numerical study using Discrete Duality Finite Volume

# [CT038]

**Session Time & Room****Classification**

## [02692] Discovering extremal domains via shape optimization for passive tracers

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G602__**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__**Format**: Talk at Waseda University**Author(s)**:**Manuchehr Aminian**(California State Polytechnic University Pomona)

## [02566] A spherically symmetric and steady flow describing the motion of a viscous gaseous star

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G602__**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__**Format**: Online Talk on Zoom**Author(s)**:**Morimichi Umehara**(University of Miyazaki)

## [02581] Well-Posedness and smoothness of geometric flows with nonlinear boundary conditions

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G602__**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__**Format**: Talk at Waseda University**Author(s)**:**Daniel Goldberg**(Technion-Israel Institute of Technology)

## [01080] About Thermistor Problem: numerical study using Discrete Duality Finite Volume

**Session Time & Room**:__5D__(Aug.25, 15:30-17:10) @__G602__**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)