講座主題：Uniqueness and numerical methods for inverse Stokes problems
專(zhuān)家姓名：楊家青
工作單位：西安交通大學(xué)
講座時(shí)間：2024年05月29日15:00-16:00
講座地點(diǎn)：數(shù)學(xué)與信息科學(xué)學(xué)院341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this talk, we consider an inverse Stokes problem in a bounded domain with a discontinuous viscosity coefficient. By analyzing the singularity of the Dirichlet Green's function near the interface in combination with constructing a well-posed Stokes-Brinkman system in a small domain, we prove a global uniqueness theorem that the discontinuous viscosity coefficient can be determined by the local Dirichlet-to-Neumann map defined on an arbitrary small open subset of the boundary. Moreover, we also consider an inverse Stokes problem of reconstructing a bounded solid in an unbounded Stokes fluid, where the well-known LSM, FM and GLSM are extended from the wave equation into the Stokes equation by only taking the velocity fields in a certain domain. Finally, some numerical results are presented to illustrate the effectiveness of the inversion algorithms.
主講人介紹：
楊家青，西安交通大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授/博導(dǎo)，研究方向?yàn)榉磫?wèn)題的數(shù)學(xué)理論與計(jì)算方法。目前，在SIAM J. Appl. Math., SIAM J.Numer. Anal., SIAM J. Sci.Comput., SIAM J. Imaging Sci., JCP，JDE，IPI等國(guó)際期刊發(fā)表論文近四十篇。主持國(guó)家自然科學(xué)基金優(yōu)秀青年科學(xué)基金項(xiàng)目，是國(guó)家重點(diǎn)研發(fā)計(jì)劃的課題負(fù)責(zé)人；曾獲陜西省百人計(jì)劃青年項(xiàng)目、中國(guó)工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)“CSIAM應(yīng)用數(shù)學(xué)青年科技獎(jiǎng)”；山東省自然科學(xué)二等獎(jiǎng)等。
