On approximation of coefficient inverse problems for differential equations in functional spaces. (English. Russian original) Zbl 1434.35280
J. Math. Sci., New York 230, No. 6, 823-906 (2018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 133 (2017).
Summary: This paper is devoted to the theory of approximation of coefficient inverse problems for differential equations of parabolic, elliptic, and hyperbolic types in functional spaces. We present general statements of problems and their approximations and review results obtained earlier in the literature.
MSC:
| 35R30 | Inverse problems for PDEs |
| 65J22 | Numerical solution to inverse problems in abstract spaces |
Keywords:
abstract differential equation; abstract hyperbolic problem; abstract elliptic problem; abstract parabolic problem; \(C_0\)-semigroup; Banach space; semidiscretization; inverse overdetermined problem; finite-difference scheme; discrete semigroupReferences:
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