一类带有趋化性扩散的细菌模型一致有界解的整体存在性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (2): 409-418.

一类带有趋化性扩散的细菌模型一致有界解的整体存在性

曲风龙¹, 王玉泉²

1.烟台大学数学与信息科学学院山东烟台 264005;
2.首都师范大学数学科学学院北京 100037

收稿日期:2012-06-17 修回日期:2013-10-21 出版日期:2014-04-25 发布日期:2014-04-25
基金资助:
国家自然科学基金(10671131, 11201402, 11201266)、北京自然科学基金(1092006)和天元基金(11026098, 11026150)资助.

The Interior Transmission Problem for Isotropic Maxwell Equations and Some Estimates on the Index of Refraction

QU Feng-Long¹, WANG Yu-Quan²

1.School of Mathematics and Informational Science, Yantai University, Shandong Yantai 264005;
2.Department of Mathematics, Capital Normal University, Beijing 100037

Received:2012-06-17 Revised:2013-10-21 Online:2014-04-25 Published:2014-04-25
Supported by:
国家自然科学基金(10671131, 11201402, 11201266)、北京自然科学基金(1092006)和天元基金(11026098, 11026150)资助.

摘要/Abstract

摘要：

考虑二维空间中一类带有趋化性扩散的生物模型的一致有界解的整体存在性. 利用细致的能量估计、不同希尔伯特空间(包括V₂(Q_{t, t}₊₁)、W^{1, 2}_{p, p}(Qt_{, t}₊₁)、L_{p, q}(Q_{t, t}₊₁))的先验估计以及一致Gronwall不等式, 证明了一类带有出生率和死亡率项的生物模型的一致有界解的整体存在性.

关键词: 趋化性, 整体存在性, 一致有界性

Abstract:

This paper is concerned with the global existence of uniformly bounded solutions for a class of chemotaxis models in two dimensional spaces. By using detailed energy estimates, some a priori estimates in different types of spaces including V₂(Q_{t, t}₊₁)、W^{1, 2}_{p, p}(Qt_{, t}₊₁)、L_{p, q}(Q_{t, t}₊₁)) and by applying uniform Gronwall inequality, we can prove the global existence of uniformly bounded solutions for a class of chemotactic systems with the proliferation term which involves both growth and death of the bacteria.

Key words: Chemotaxis, Global existence, Uniformly boundedness

中图分类号:

35K50

曲风龙, 王玉泉. 一类带有趋化性扩散的细菌模型一致有界解的整体存在性[J]. 数学物理学报, 2014, 34(2): 409-418.

QU Feng-Long, WANG Yu-Quan. The Interior Transmission Problem for Isotropic Maxwell Equations and Some Estimates on the Index of Refraction[J]. Acta mathematica scientia,Series A, 2014, 34(2): 409-418.

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