This paper deals with a parabolic system in a multi dimentional bounded domain ΩR n with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distri...This paper deals with a parabolic system in a multi dimentional bounded domain ΩR n with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distribution at any intermediate moment from the heat distribution measurements in arbitrary accessible subdomain ωΩ at some time interval. Our main result is the Hlder stability estimate in the inverse problem and the proof is completed with a Carleman estimate and a eigenfunction expansion for parabolic equations.展开更多
In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved u...In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved.展开更多
This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel.This equation is accompanied by a Robin boundary condition.The miss...This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel.This equation is accompanied by a Robin boundary condition.The missing kernel can be recovered from an additional global measurement in integral form.In this contribution,an error analysis is performed for a time-discrete numerical scheme based on Backward Euler’s Method.The theoretical results are supported by some numerical experiments.展开更多
文摘This paper deals with a parabolic system in a multi dimentional bounded domain ΩR n with the smooth boundary Ω. We discuss an inverse parabolic problem of determining the indirectly measurable internal heat distribution at any intermediate moment from the heat distribution measurements in arbitrary accessible subdomain ωΩ at some time interval. Our main result is the Hlder stability estimate in the inverse problem and the proof is completed with a Carleman estimate and a eigenfunction expansion for parabolic equations.
文摘In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved.
基金This work was supported by Multiscale Modelling of Electrical En-ergy Systems,IAP P7/02-project of the Belgian Science Policy.
文摘This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel.This equation is accompanied by a Robin boundary condition.The missing kernel can be recovered from an additional global measurement in integral form.In this contribution,an error analysis is performed for a time-discrete numerical scheme based on Backward Euler’s Method.The theoretical results are supported by some numerical experiments.
