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- W2181344213 abstract "We consider a linear heat equation involving a fractional deriv- ative in time, with a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution for a problem with an over-determining condition of integral type. We prove the existence and uniqueness of the solution, and its continuous dependence on the data. temperature '(x) and the source term F (x;t) are given and continuous. Letting the source term have the form F (x;t) = a(t)f(x;t), then the inverse problem consists of determining a source term a(t) and the temperature distribu- tion u(x;t), from the initial temperature '(x) and boundary conditions (1.3). This problem is not uniquely solvable. The inverse problem of determining a(t) was al- ready considered in the literature for parabolic equations, see for example (5) and (2)." @default.
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- W2181344213 date "2013-12-01" @default.
- W2181344213 modified "2023-09-25" @default.
- W2181344213 title "Determination of a source term for a time fractional diffusion equation with an integral type over-determining condition" @default.
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