2022-08-09T02:27:19Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000040452021-03-01T19:48:22Zカーレマン評価を用いた、粘弾性論・材料科学・個体群動態学における偏微分方程式系の係数決定逆問題についてCoefficient inverse problems for partial differential equations in the viscoelasticity, the material science and population dynamics by Carleman estimatesUesaka, Masaaki9334410University of Tokyo (東京大学)博士(数理科学)In this paper, we consider coefficient inverse problems in the viscoelasticity,the material science and the population studies and prove the stability ofthese problem by an a priori weighted L2-norm estimate which is called aCarleman estimate.In Chapter 1, an inverse problem of determining coefficients in a viscoelasticmodel which is called Kelvin-Voigt model is discussed. The dataavailable to us is a Cauchy data on subboundary. We prove that with twoappropriate measurements, we can obtain a Holder stability estimate of the inverse problem.In Chapter 2, we discuss the determination of a thermal conductivity anda mobility in the linearized phase field model with measurement of only onecomponent in a small domain. Our result is the Lipschitz stability estimate of this problem.In Chapter 3, we consider the coefficient inverse problem of the structuredpopulation model. In the structured population model, an age andan individual size as well as a spatial position and time are considered asindepenent variables and then the equation has a special form. We prove a Carleman estimate for this equation and obtain a stability estimate for theinverse problem.thesis2011-03-242011-03-24application/pdfapplication/pdf甲第27184号https://repository.dl.itc.u-tokyo.ac.jp/record/4045/files/UesakaM_23_3_PhD_a.pdfhttps://repository.dl.itc.u-tokyo.ac.jp/record/4045/files/UesakaM_23_3_PhD_b.pdfeng