Recent results for the logarithmic Keller-Segel-Fisher/KPP System
We consider a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. It is a 2 by 2 system describing the interaction of cells and a chemical signal. We study Cauchy problem with finite initial data, i.e., without the commonly used smallness assumption on initial pert...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2019-10-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44494 |
| Summary: | We consider a Keller-Segel type chemotaxis model with logarithmic sensitivity and logistic growth. It is a 2 by 2 system describing the interaction of cells and a chemical signal. We study Cauchy problem with finite initial data, i.e., without the commonly used smallness assumption on initial perturbations around a constant ground state. We survey a sequence of recent results by the authors on the existence of global-in-time solution, long-time behavior, vanishing coefficient limit and optimal time decay rates of the solution.
|
|---|---|
| ISSN: | 0037-8712 2175-1188 |