| Title: | Finite energy solutions to the 6D Fujita equation in the Sobolev critical case |
| Time: | 16:00:00 - |
| Zoom Link: | https://hkust.zoom.us/j/97692499717 |
| Abstract: | We discuss the dynamics near the ground states for the 6D Fujita equation. This result presents a 6D version of the classification in a higher dimensional setting, obtained by Charles Collot - Frank Merle - Pierre Raphael (2017). In contrast to their results (they assume only that π’! β π»Μ"(π #)), our result requires the additional integrability conditions on the initial dataπ’! β πΏ$(π #). We also point out that the assumption π’! β π»Μ"(π #) alone is not sufficient for the stabilization of the solution in the case π = 6. |
| Title: | Isomonodromy Equations and the Inverse Monodromy Problem |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Room 5506 (Lift 25/26) |
| Abstract: | In this talk, we will introduce our recent work on some isomonodromy equations. These can be regarded as higher PainlevΓ© equations. Our main result concerns the asymptotic behavior of their generic solutions; we also provide series solutions derived from the monodromy data and use this approach to study the inverse monodromy problem. |
| Title: | Overlapping Multiplicative Schwarz Preconditioning for Linear and Nonlinear Systems |
| Time: | 10:00:00 - 11:00:00 |
| Place: | Room 1409 (Lift 25/26) |
| Abstract: | For linear and nonlinear systems arising from the discretization of PDEs, multiplicative Schwarz preconditioners can be defined based on subsets of the unknowns that derive from domain decomposition, field splitting, or other collections of conveniently solved subproblems, and are well established theoretically for nonoverlapping subsets. For overlapping subsets, establishing the equivalence of the preconditioned and original iterations is less trivial. We derive herein an explicit formulation for a variety of multiplicative Schwarz preconditioners including overlaps representative of interfacial and bulk coupling in multiphysics systems, thus extending theoretical support for the nonlinear multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm to these classes. For nonlinear multiplicative Schwarz preconditioners with overlaps, we illustrate the performance through numerical experiments involving applications such as a shocked duct flow and a natural convection cavity flow. We begin with a broad introduction to nonlinear preconditioning to set the context for those new to the technique. This is joint work with D. E. Keyes, L. Liu, and H. Yu. |
| Title: | Book Launch - Empowering K-12 Education with AI: Preparing for the Future of Education and Work |
| Time: | 16:00:00 - 17:00:00 |
| Place: | Room B5, Ho Tim Building |
| Zoom Link: | https://cloud.itsc.cuhk.edu.hk/webform/view.php?id=13708669 |
| Abstract: | In this book launch, Prof, Chiu Kin FungThomas will discuss how Al impact K-12education in two areas: Al education, andAl in education. This book examines theopportunities and challenges of theseimpacts for teachersandstudents,proposes aframework and a set ofprinciples for the two areas with examples.This book is an essential and thought-provoking read for anyone wish toembrace Al to prepare K-12 students fortheir future education and the workforce,This event welcome school teachers,education officers,researchstudents,teacher educators,andeducationalresearchers |