{"title":"正则化 p-Stokes 方程的系数识别","authors":"","doi":"10.1016/j.nonrwa.2024.104197","DOIUrl":null,"url":null,"abstract":"<div><p>The Antarctic and Greenland ice sheet simulation is challenging due to unknown parameters in the <span><math><mi>p</mi></math></span>-Stokes equations. In this work, we prove the existence of a solution to a parameter identification for the ice rheology and the friction coefficient. Additionally, we verify Gâteaux differentiability of the coefficient-to-state operator by extending a similar result for distributed control. Moreover, we have more complicated boundary conditions. We only have to add a small diffusion term and assume the nonlinear exponent, which is given in applications, to be small enough to obtain the results. Finally, we state the adjoint equation and prove existence and uniqueness of a solution for this equation.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824001366/pdfft?md5=d952cd15048b83ceaab49299a4863fc2&pid=1-s2.0-S1468121824001366-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Coefficient identification of the regularized p-Stokes equations\",\"authors\":\"\",\"doi\":\"10.1016/j.nonrwa.2024.104197\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The Antarctic and Greenland ice sheet simulation is challenging due to unknown parameters in the <span><math><mi>p</mi></math></span>-Stokes equations. In this work, we prove the existence of a solution to a parameter identification for the ice rheology and the friction coefficient. Additionally, we verify Gâteaux differentiability of the coefficient-to-state operator by extending a similar result for distributed control. Moreover, we have more complicated boundary conditions. We only have to add a small diffusion term and assume the nonlinear exponent, which is given in applications, to be small enough to obtain the results. Finally, we state the adjoint equation and prove existence and uniqueness of a solution for this equation.</p></div>\",\"PeriodicalId\":49745,\"journal\":{\"name\":\"Nonlinear Analysis-Real World Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001366/pdfft?md5=d952cd15048b83ceaab49299a4863fc2&pid=1-s2.0-S1468121824001366-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Real World Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001366\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001366","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Coefficient identification of the regularized p-Stokes equations
The Antarctic and Greenland ice sheet simulation is challenging due to unknown parameters in the -Stokes equations. In this work, we prove the existence of a solution to a parameter identification for the ice rheology and the friction coefficient. Additionally, we verify Gâteaux differentiability of the coefficient-to-state operator by extending a similar result for distributed control. Moreover, we have more complicated boundary conditions. We only have to add a small diffusion term and assume the nonlinear exponent, which is given in applications, to be small enough to obtain the results. Finally, we state the adjoint equation and prove existence and uniqueness of a solution for this equation.
期刊介绍:
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.