Session Time & Room : 5D (Aug.25, 15:30-17:10) @G501
Type : Proposal of Minisymposium
Abstract : The aim of this mini-symposium is to overview contemporary theory and applications on homogenization by specialists from various areas.
Short time behavior of particles in inhomogeneous media may depend on the location of particles, whereas their long time behavior often tends to be homogeneous due to the averaging effects. Such an averaging process is called homogenization.
Homogenization has been a very active research area in mathematics and applied mathematics for a long time. We invite specialists from several fields, including PDE, probability, analysis and applied mathematics. We exchange ideas and discuss various aspects on homogenization.
[01750] On the rate of convergence in homogenization of time fractional Hamilton-Jacobi equations
Format : Talk at Waseda University
Author(s) :
Hiroyoshi Mitake (University of Tokyo)
Abstract : In this talk, we consider periodic homogenization for time fractional Hamilton-Jacobi equations. By using the perturbed test function method, we establish the convergence, and give estimates on the rate of convergence. A main difficulty is the incompatibility between the function used in the doubling variable method, and the non-locality of the Caputo derivative. Our approach is to provide a lemma to prove the rate of convergence without the doubling variable method with respect to the time variable, which is a key ingredient. This is a joint work with Shoichi Sato (U. Tokyo).
[01811] Discrete approximation of higher degree Laplacians
Format : Talk at Waseda University
Author(s) :
Jun Masamune (Tohoku University)
Hiroki Fukagawa (DeepFlow Inc)
Abstract : In this talk, we review some basic ideas in the theory of homogenization
and discuss recent progress in the theory and applications of discrete approximation
of equations involving, possibly higher degree, Laplacian. The talk is based
on a collaborative effort with Hiroki Fukagawa from DeepFlow Inc.
[03559] Homogenization of the rate-independent evolution of a random heterogeneous, elasto-plastic spring network
Format : Talk at Waseda University
Author(s) :
Stefan Neukamm (TU Dresden)
Abstract : We consider a periodic network composed of elasto-plastic spring with stationary and ergodic coefficients, described as a evolutionary rate independent system (ERIS) and derive a homogenized, continuum model as evolutionary Gamma-limit. The limit can be described as a generalized Prandtl-Ishlinskii hysteresis model and we analyse a corresponding RVE approximation.
