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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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