# Difference between revisions of "PDE Geometric Analysis seminar"

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VV B239 4:00pm | VV B239 4:00pm | ||

| Jaeyoung Byeon (KAIST) | | Jaeyoung Byeon (KAIST) | ||

− | |[[Jaeyoung Byeon| Colloquium: ]] | + | |[[Jaeyoung Byeon| Colloquium: Patterns formation for elliptic systems with large interaction forces]] |

| Rabinowitz | | Rabinowitz | ||

|- | |- | ||

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===Mihaela Ifrim=== | ===Mihaela Ifrim=== | ||

+ | |||

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

+ | |||

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

+ | |||

+ | Abstract : Nonlinear elliptic systems coming from nonlinear Schroedinger systems have simple looking reaction terms whose corresponding energy can be expressed as quadratic forms in terms of density functions. The entries of the matrix for the quadratic form represent interaction forces between components for a system. If the signature of an entry is positive, the force between two components is attraction; on the other hand, if it is negative, it is repulsion. 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 general patterns formation structure for systems with large number of components, I would like to illustrate a phenomenon for systems with two components, and for systems with three components introduce some recent results of several phenomena depending on the network structure of attraction and repulsion between components. |

## Revision as of 08:58, 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 coming from nonlinear Schroedinger systems have simple looking reaction terms whose corresponding energy can be expressed as quadratic forms in terms of density functions. The entries of the matrix for the quadratic form represent interaction forces between components for a system. If the signature of an entry is positive, the force between two components is attraction; on the other hand, if it is negative, it is repulsion. 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 general patterns formation structure for systems with large number of components, I would like to illustrate a phenomenon for systems with two components, and for systems with three components introduce some recent results of several phenomena depending on the network structure of attraction and repulsion between components.