On some classes of inverse problems for parabolic and elliptic equations

Abstract

We study solvability of inverse problems of finding the right-hand side together with a solution itself for vector-valued parabolic and elliptic equations. The usual boundary conditions are supplemented with the overdetermination conditions that are the values of a solution on some system of surfaces.

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Pyatkov, S.G., Tsybikov, B.N. On some classes of inverse problems for parabolic and elliptic equations. J. Evol. Equ. 11, 155–186 (2011). https://doi.org/10.1007/s00028-010-0087-6

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Mathematics Subject Classification (2000)

  • Primary 35R30
  • Secondary 35K90
  • 35K40
  • 35J45

Keywords

  • Parabolic equation
  • Elliptic equation
  • Inverse problem
  • Control problem
  • Heat and mass transfer