Restricted Research - Award List, Note/Discussion Page
Fiscal Year: 2023
2338 The University of Texas at San Antonio (144226)
Principal Investigator: Gui,Changfeng
Total Amount of Contract, Award, or Gift (Annual before 2011): $ 380,575
Exceeds $250,000 (Is it flagged?): Yes
Start and End Dates: 8/1/22 - 7/31/25
Restricted Research: YES
Academic Discipline: none
Department, Center, School, or Institute: COS MATH
Title of Contract, Award, or Gift: SCI-12209 Further Studies on the Mean Field Equation and Allen-Cahn Equation
Name of Granting or Contracting Agency/Entity:
National Science Foundation (LOC)
CFDA Link: NSF
47.049
Program Title:
none
CFDA Linked: Mathematical and Physical Sciences
Note:
SAMs 1.1.1 In this research award, the PI plans to further investigate stable solutions, saddle solutions and finite morse index solutions of Allen-Cahn type and mean field equations, including the classic scalar equations with double well potentials and vector-valued equations with multiple well potentials. The PI will focus on the symmetry of stable solutions, the existence of special unstable solutions with finite Morse index, and the relation between the level sets of solutions and minimal surfaces. The PI intends to use various identities as well as Morse index information to develop new approach for these non monotone, non minimizing solutions. The long term goal of the project is to understand general entire solutions for both scalar and vector-valued Allen-Cahn equations and the stability and dynamics of triple junctions or quadruple junctions, and classification of all finite morse index solutions of the mean field equation on the two dimensional sphere and flat tori. The nodal sets or singularities of the solutions of Allen-Cahn equation will receive special attention in the study since they not only play an important role in the theoretic analysis of the equation, they also represent in applications the interfaces or junctions of interfaces of different phases or grain boundaries in materials such as crystalline alloys.
Discussion: No discussion notes