The paper is concerned with some chemotaxis model au/at=DV（u↓△ln（u/w））＋u（a-bu）,aw/at--f（u, w）. To study the behavior of the solution, some function transformations are intro- duced, and the main tool is sup...The paper is concerned with some chemotaxis model au/at=DV（u↓△ln（u/w））＋u（a-bu）,aw/at--f（u, w）. To study the behavior of the solution, some function transformations are intro- duced, and the main tool is sup-sub-solution method. The result shows that, whether the solution blows up in finite time depends on the parameters and the initial data. As the chemical substance w has linear growth, f（u,w）=βu-δw, where β〉0, δ〉0, and α＋δ〉0, wherein the solution exists globally. However, as w possesses ex- ponential growth, f（u,w）=（βu-δ）w, wherein both u and w share the same blowup point and time if the solution blows up in finite time.展开更多
基金Supported by the National Natural Science Foundation of China(10471108)
文摘The paper is concerned with some chemotaxis model au/at=DV（u↓△ln（u/w））＋u（a-bu）,aw/at--f（u, w）. To study the behavior of the solution, some function transformations are intro- duced, and the main tool is sup-sub-solution method. The result shows that, whether the solution blows up in finite time depends on the parameters and the initial data. As the chemical substance w has linear growth, f（u,w）=βu-δw, where β〉0, δ〉0, and α＋δ〉0, wherein the solution exists globally. However, as w possesses ex- ponential growth, f（u,w）=（βu-δ）w, wherein both u and w share the same blowup point and time if the solution blows up in finite time.
