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Inverse problems for the stationary and pseudoparabolic equations of diffusion. (English) Zbl 1447.35385
Summary: The identification of an unknown coefficient in the lower term of pseudoparabolic differential equation of diffusion \((u+\eta Mu)_t + Mu+ku=f\) and elliptic second-order differential equation \(Mu+ku=f\) with the Dirichlet boundary condition is considered. The identification of \(k\) is based on an integral boundary data. The local existence and uniqueness of generalized strong solutions for the inverse problems are proved. The stability estimates are exposed.
MSC:
35R30 Inverse problems for PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35J25 Boundary value problems for second-order elliptic equations
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