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陶有山教授学术讲座预告

讲座题目:  Chemotaxis models in complex frameworks

讲座时间:  2016年06月22日下午3:00-5:00

讲座地点:  理学院9层学术报告厅 (924)

主讲人:  陶有山教授

内容摘要:  
Motivated by various biological processes, this talk first briefly introduces five typical chemotaxis models: chemotaxis-growth model, chemotaxis-haptotaxis model, chemotaxis-fluid model with signal consumption, chemotaxis-fluid model with chemical production, and chemotaxis model with indirect signal production.

Then this talk focuses a chemotaxis-haptotaxis model for cancer invasion, which describes the mutual interactions between cancer cells, enzymes and extracellular matrix. The system consists of two parabolic PDEs, one of which possesses two cross-diffusion terms reflecting the biased movements of cells due to chemotaxis and haptotaxis, coupled with an ODE. Inspired by some new observations or approaches toward this system, we could discuss the boundedness and asymptotic behavior of the solutions.

       This talk also addresses a chemotaxis system with indirect signal production, which models the aggregation behavior of the Mountain Pine Beetle in forest habitat. In the two-dimensional case, it is shown that this system exhibits a novel type of critical mass phenomenon with regard to the formation of singularities, which drastically differs from the well-known threshold  property of the classical Keller-Segel system, in that it refers to blow-up in infinite time rather than in finite time. In the three-dimensional setting, any arbitrarily small logistic damping is sufficient to prevents blow-up of solutions, which strikingly differs from the classical Keller-Segel system once again
主讲简介:  
 陶有山, 东华大学教授。他1986年获得南京大学学士学位,1992年获得复旦大学理学硕士学位,1995年毕业于苏州大学并获博士学位。曾多次在美国俄亥俄州立大学、日本东京大学进行学术访问。
陶有山教授研究方向为偏微分方程、生物数学,在趋向性数学模型的研究、前列腺癌间隙性雄激素剥夺治疗的数学模型研究、及肿瘤生长及其干预治疗的数学模型研究方面取得了一系列成果。发表学术论文60余篇、主持国家基金及省部级项目10余项。现担任国际学术 期刊《Nonlinear Anal. RWA》的编委及 Springer 丛书系《Modelling and simulation in science,engineering and technology》的编委.
正文

        Motivated by various biological processes, this talk first briefly introduces five typical chemotaxis models: chemotaxis-growth model, chemotaxis-haptotaxis model, chemotaxis-fluid model with signal consumption, chemotaxis-fluid model with chemical production, and chemotaxis model with indirect signal production.

Then this talk focuses a chemotaxis-haptotaxis model for cancer invasion, which describes the mutual interactions between cancer cells, enzymes and extracellular matrix. The system consists of two parabolic PDEs, one of which possesses two cross-diffusion terms reflecting the biased movements of cells due to chemotaxis and haptotaxis, coupled with an ODE. Inspired by some new observations or approaches toward this system, we could discuss the boundedness and asymptotic behavior of the solutions.

       This talk also addresses a chemotaxis system with indirect signal production, which models the aggregation behavior of the Mountain Pine Beetle in forest habitat. In the two-dimensional case, it is shown that this system exhibits a novel type of critical mass phenomenon with regard to the formation of singularities, which drastically differs from the well-known threshold  property of the classical Keller-Segel system, in that it refers to blow-up in infinite time rather than in finite time. In the three-dimensional setting, any arbitrarily small logistic damping is sufficient to prevents blow-up of solutions, which strikingly differs from the classical Keller-Segel system once again.

 


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