An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed w...An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed with aids of an optimal adjoint problem and a suitable topology.展开更多
An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non...An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non-stationary transport equation,a global Lipschitz stability for the inverse problem was proved.展开更多
In this paper,we consider an inverse time-dependent source problem of heat conduction equation.Firstly,the ill-posedness and conditional stability of this inverse source problem is analyzed.Then,a finite difference in...In this paper,we consider an inverse time-dependent source problem of heat conduction equation.Firstly,the ill-posedness and conditional stability of this inverse source problem is analyzed.Then,a finite difference inversion method is proposed for reconstructing the time-dependent source from a nonlocal measurement.The existence and uniqueness of the finite difference inverse solutions are rigorously analyzed,and the convergence is proved.Combined with the mollification method,the proposed finite difference inversion method can obtain more stable reconstructions from the nonlocal data with noise.Finally,numerical examples are given to illustrate the efficiency and convergence of the proposed finite difference inversion method.展开更多
基金National Natural Science Foundation of China No. 10471080.
文摘An inverse problem of determining magnitude of groundwater pollution in a hydrologic region is investigated. By applying integral identity methods, a conditional stability for the inverse problem here is constructed with aids of an optimal adjoint problem and a suitable topology.
文摘An inverse problem of determining the source term of the non-stationary transport equation was considered.The extra lateral boundary condition was chosen as the observation data.Based on a Carleman estimate on the non-stationary transport equation,a global Lipschitz stability for the inverse problem was proved.
基金supported by National Natural Science Foundation of China(11561003,11661004,11761007)Natural Science Foundation of Jiangxi Province(20161BAB201034)Foundation of Academic and Technical Leaders Program for Major Subjects in Jiangxi Province(20172BCB22019)。
文摘In this paper,we consider an inverse time-dependent source problem of heat conduction equation.Firstly,the ill-posedness and conditional stability of this inverse source problem is analyzed.Then,a finite difference inversion method is proposed for reconstructing the time-dependent source from a nonlocal measurement.The existence and uniqueness of the finite difference inverse solutions are rigorously analyzed,and the convergence is proved.Combined with the mollification method,the proposed finite difference inversion method can obtain more stable reconstructions from the nonlocal data with noise.Finally,numerical examples are given to illustrate the efficiency and convergence of the proposed finite difference inversion method.
