This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse probl...This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.展开更多
基金supported by the National Natural Science Foundation of China(No.12171036)Beijing Natural Science Foundation(No.Z210001)the NSF of China No.11971221,Guangdong NSF Major Fund No.2021ZDZX1001,the Shenzhen Sci-Tech Fund Nos.RCJC20200714114556020,JCYJ20200109115422828 and JCYJ20190809150413261,National Center for Applied Mathematics Shenzhen,and SUSTech International Center for Mathematics.
文摘This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear PDEs.Moreover,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption isotherms.The stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.
