Partial reconstruction of the source term in a linear parabolic initial value problem. (English) Zbl 1178.35379
The reconstruction of source term for a linear parabolic problem is of great importance. Generally, it is very hard to determine the source term in general form from some specified measurement data. Therefore we are led to identify the partial information of the source term in the sense that the source term has some special decomposition.
This paper considers a source inverse problem in this category for a general parabolic system from some integral data of the solution. The new ingredients of this problem are the spatial variable decompositions \((x,y)\in \mathbb{R}^m\times \mathbb{R}^n\) for both the elliptic operator and the source term, which are generalizations of the previous works. Under general assumptions on elliptic operators and unknown source term in the equation, the author proves the existence and uniqueness results. It is still an open problem to consider a stable inversion scheme for this problem.
This paper considers a source inverse problem in this category for a general parabolic system from some integral data of the solution. The new ingredients of this problem are the spatial variable decompositions \((x,y)\in \mathbb{R}^m\times \mathbb{R}^n\) for both the elliptic operator and the source term, which are generalizations of the previous works. Under general assumptions on elliptic operators and unknown source term in the equation, the author proves the existence and uniqueness results. It is still an open problem to consider a stable inversion scheme for this problem.
Reviewer: Jijun Liu (Nanjing)
MSC:
| 35R30 | Inverse problems for PDEs |
| 35N10 | Overdetermined systems of PDEs with variable coefficients |
| 35K30 | Initial value problems for higher-order parabolic equations |
References:
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