Finite Morse Index Solutions of AllenCahn Equation
Finite Morse Index Solutions of AllenCahn Equation

Changfeng Gui, University of Texas at San Antonio
Fine Hall 214
AllenCahn equation arises in the mathematical study of phase transition. Despite its seemingly simple appearance, the equation has connections to minimal surfaces theory and displays a very rich structure involving deep mathematics. In this talk, I will give a review of the history of the equation, and discuss the existence, symmetry and classification of finite Morse index solutions of the AllenCahn equation. In particular, I will report some recent results on the classification of Morse index solutions in low dimensions.