講座題目：Some progress for the global existence and boundedness of high-dimensional chemotaxis-haptotaxis models with re-establishment mechanisms
講座時(shí)間：2024年6月25日（星期二）下午15:30-16:20
講座地點(diǎn)：kaiyun開云官方網(wǎng)站犀浦校區(qū)3號(hào)教學(xué)樓 X30423
主講人簡(jiǎn)介：
鄭甲山，煙臺(tái)大學(xué)教授，碩士生導(dǎo)師, 山東省杰出青年基金和山東省優(yōu)秀青年基金獲得者，獲得首屆山東數(shù)學(xué)會(huì)青年數(shù)學(xué)獎(jiǎng)。主要面向生物科學(xué)與力學(xué)及物理學(xué)、醫(yī)學(xué)與流體動(dòng)力學(xué)等領(lǐng)域偏微分方程的數(shù)學(xué)問題，主要開展趨化-(納維)-斯托克斯相關(guān)模型、非線性拋物型方程與流體動(dòng)力學(xué)方程等學(xué)科領(lǐng)域的熱點(diǎn)問題研究。主持（完成）山東省杰出青年基金、山東省優(yōu)秀青年基金、國(guó)家自然科學(xué)基金、中國(guó)博士后特別資助和博士后面上資助、山東省自然科學(xué)青年基金等多項(xiàng)基金。并以第一或者通訊作者在《CVPDE》(3篇)、《M3AS》(1篇)、《JDE》(13篇)、《Nonlinearity》(2篇)等頂級(jí)期刊發(fā)表SCI論文70余篇，包含4篇 ESI 高被引論文，連續(xù)三年入選斯坦福大學(xué)發(fā)布的“全球前2%頂尖科學(xué)家榜單”。已被包括國(guó)際數(shù)學(xué)家大會(huì)45分鐘報(bào)告人、長(zhǎng)江學(xué)者特聘教授、頂級(jí)期刊《M3AS》主編、《JDE》等著名雜志編委在內(nèi)的多名數(shù)學(xué)專家引用總次數(shù)800余次。應(yīng)國(guó)際物理科學(xué)院院士Hari M. Srivastava教授所邀在 Springer雜志合作撰寫趨化-N-S相關(guān)模型的專著。應(yīng)邀擔(dān)任國(guó)際期刊《American Journal of Applied Mathematics》、《Mathematics and Computer Science 》和《World Journal of Mathematics and Statistics》和《Applied and Computational Mathematics》的編委；應(yīng)邀參加中國(guó)數(shù)學(xué)會(huì)第十三次全國(guó)代表大會(huì)并作報(bào)告；應(yīng)邀擔(dān)任美國(guó)《Mathematical Reviews》評(píng)論員和德國(guó)《數(shù)學(xué)文摘》評(píng)論員。
講座內(nèi)容簡(jiǎn)介：
The chemotaxis--haptotaxis model with remodeling of non-diffusible attractant
is considered in a bounded domain Ω??3 with smooth boundary, where X>0,ξ>0 as well as η>0 are given parameters. This model is initially proposed by Chaplain and Lolas (2006) \cite{Chaplain7} to describe the interactions between cancer cells, the matrix degrading enzyme and the host tissue in a process of cancer cell invasion of tissue (extracellular matrix). Assume that f(u,w)=μu(1?u?w). The paper develops an analytical approach which consists in a combination of energy-based arguments and maximal Sobolev regularity theory, and which allows for the construction of global bounded classical solutions to an associated initial-boundary value problem under the assumption that μ is appropriately large. After conducting thorough research and incorporating the essence of numerous prior studies, this paper not only extends the findings of these previous works (see {Remark} 1.1) but also deepens our understanding of chemotaxis-haptotaxis models. Notably, we have successfully demonstrated for the first time the boundedness of solutions in a three-dimensional chemotaxis-haptotaxis model featuring the remodeling of non-diffusible attractants. This significant discovery undoubtedly adds new dimensions to the theoretical framework of chemotaxis-haptotaxis models. Furthermore, the achievement of this milestone not only broadens the scope of research in chemotaxis-haptotaxis models but also provides researchers in related fields with fresh perspectives and ideas, paving a new path for future studies. At the same time, some extensions will be made to this model, and some methods of this model will be used to summarize and promote relevant models.
