Properties of solutions of parabolic equations with unknown coefficients. (English. Russian original) Zbl 1219.35357
Differ. Equ. 47, No. 1, 60-68 (2011); translation from Differ. Uravn. 47, No. 1, 60-69 (2011).
Summary: We justify statements in Hölder classes for ill-posed inverse problems with terminal observation for parabolic equations with unknown coefficients multiplying lower-order terms or lower-order derivatives. On the basis of the duality principle, we prove sufficient conditions for the uniqueness of solutions in these classes. We present examples of instability and loss of uniqueness.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35K99 | Parabolic equations and parabolic systems |
| 35B35 | Stability in context of PDEs |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
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