Stability analysis for determining a source term in a 1-D advection-dispersion equation. (English) Zbl 1111.35122

Summary: We are concerned with conditional stability for an inverse problem of deciding source terms \(f(x)\) in a 1D advection-dispersion equation \[ \frac{\partial c}{\partial t}-D_L\frac{\partial^2c}{\partial x^2}+u \frac{\partial c}{\partial x}=\alpha(t)f(x) \] by final observations \(c(x,T)=c_T(x)\), \(0\leq x\leq\ell\). The inverse problem here is based on a mathematical model derived from a real world case in a geological region in Shandong province, China. With an integral identity and analysis for a normal Sturm-Liouville problem, conditional stability for the inverse problem is proved.


35R30 Inverse problems for PDEs
86A22 Inverse problems in geophysics
35K15 Initial value problems for second-order parabolic equations
Full Text: DOI


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