# Difference between revisions of "PDE Geometric Analysis seminar"

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===Jaeyoung Byeon=== | ===Jaeyoung Byeon=== | ||

− | Title : Patterns formation for elliptic systems with large interaction forces | + | Title: Patterns formation for elliptic systems with large interaction forces |

− | Abstract : Nonlinear elliptic systems | + | Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems. |

## Revision as of 12:05, 5 September 2017

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

## Contents

### Previous PDE/GA seminars

### Tentative schedule for Spring 2018

## PDE GA Seminar Schedule Fall 2017

date | speaker | title | host(s) |
---|---|---|---|

September 11 | Mihaela Ifrim (UW) | TBD | Kim & Tran |

September 18 | Longjie Zhang (University of Tokyo) | TBD | Angenent |

September 22,
VV B239 4:00pm |
Jaeyoung Byeon (KAIST) | Colloquium: Patterns formation for elliptic systems with large interaction forces | Rabinowitz |

September 25 | Tuoc Phan (UTK) | TBD | Tran |

September 26,
VV B139 4:00pm |
Hiroyoshi Mitake (Hiroshima University) | Joint Analysis/PDE seminar | Tran |

September 29,
VV901 2:25pm |
Dongnam Ko (CMU & SNU) | a joint seminar with ACMS: TBD | Shi Jin & Kim |

October 2 | No seminar due to a KI-Net conference | ||

October 9 | Sameer Iyer (Brown University) | TBD | Kim |

October 16 | Jingrui Cheng (UW) | TBD | Kim & Tran |

October 23 | Donghyun Lee (UW) | TBD | Kim & Tran |

November 6 | Jingchen Hu (USTC and UW) | TBD | Kim & Tran |

## Abstracts

### Mihaela Ifrim

### Jaeyoung Byeon

Title: Patterns formation for elliptic systems with large interaction forces

Abstract: Nonlinear elliptic systems arising from nonlinear Schroedinger systems have simple looking reaction terms. The corresponding energy for the reaction terms can be expressed as quadratic forms in terms of density functions. The i, j-th entry of the matrix for the quadratic form represents the interaction force between the components i and j of the system. If the sign of an entry is positive, the force between the two components is attractive; on the other hand, if it is negative, it is repulsive. When the interaction forces between different components are large, the network structure of attraction and repulsion between components might produce several interesting patterns for solutions. As a starting point to study the general pattern formation structure for systems with a large number of components, I will first discuss the simple case of 2-component systems, and then the much more complex case of 3-component systems.