Posted February 21, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
John Jairo Lopez, Tulane University
Title TBA
Abstract TBA (Host: Stephen Shipman)
Posted March 25, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:20 pm Lockett 232
Robert Lipton, Mathematics Department, LSU
Dynamic Fast Crack Growth
Nonlocal modeleling for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. The material displacement field is uniquely determined by the initial boundary value problem. The theory naturally satisfies energy balance, with positive energy dissipation rate in accord with the Clausius-Duhem inequality. Notably, these properties are not imposed but follow directly from the constitutive law and evolution equation. The limit of vanishing non-locality is analized using simple arguments from geometric measure theory to identify the limit damage energy and weak convergence methods of pde to identify the limit solution. The limiting energy is the Grifith fracture energy. The limit evolution is seen to be a weak solution for the wave equation on a time dependent domain. The exsistence theory for such solutions was recently developed in Dal Maso and Toader, J. Differ. Equ. 266, 3209–3246 (2019).
Posted December 10, 2024
Last modified January 5, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett
Yuanzhen Shao, University of Alabama
Some recent developments in the study of magnetoviscoelastic fluids
In this talk, we consider the motion of a magnetoviscoelastic fluid in a nonisothermal environment. When the deformation tensor field is governed by a regularized transport equation, the motion of the fluid can be described by a quasilinear parabolic system. We will establish the local existence and uniqueness of a strong solution. Then it will be shown that a solution initially close to a constant equilibrium exists globally and converges to a (possibly different) constant equilibrium. Further, we will show that that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria. If time permits, we will discuss some recent advancements regarding the scenario where the deformation tensor is modeled by a transport equation. In particular, we will discuss the local existence and uniqueness of a strong solution as well as global existence for small initial data.
Posted March 28, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm TBATBA
Posted March 16, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm TBATBA