| Autor: |
Mohammad Ghani |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 8, Iss 12, Pp 29872-29891 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231527?viewType=HTML |
| Popis: |
In this paper, we are interested in chemotaxis model with nonlinear degenerate viscosity under the assumptions of $ \beta = 0 $ (without the effect of growth rate) and $ u_+ = 0 $. We need the weighted function defined in Remark 1 to handle the singularity problem. The higher-order terms of this paper are significant due to the nonlinear degenerate viscosity. Therefore, the following higher-order estimate is introduced to handle the energy estimate: $ \begin{equation*} \begin{split} &U^{m-2} = \left( \frac{1}{U} \right)^{2-m}\leq Kw(z)\leq \frac{Cw(z)}{U}, \;\text{if}\;0 where $ C = max\left\{ K, L \right\} = max\left\{ \frac{a}{m-a}, (m+a)^m \right\} $ for $ a > 0 $ and $ m > a $, and $ w(z) $ is the weighted function. Then we show that the traveling waves are stable under the appropriate perturbations. The proof is based on a Cole-Hopf transformation and weighted energy estimates. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
