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Nonlinear loaded equations and inverse problems. (Russian, English) Zbl 1114.35148
Zh. Vychisl. Mat. Mat. Fiz. 44, No. 4, 694-716 (2004); translation in Comput. Math. Math. Phys. 44, No. 4, 657-678 (2004).
Inverse problems for parabolic equations with one unknown coefficient, the so-called coefficient inverse problems, are studied. Such problems are reduced to nonlocal boundary value problems for nonlinear equations of composite type. Solutions of the latter problems are proven to exist and ensure the existence of solutions to the original inverse problems.

35R30 Inverse problems for PDEs
35K25 Higher-order parabolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
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