WIAS Preprint No. 2055, (2014)

Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data


  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Lu, Shuai
  • Yamamoto, Masahiro

2010 Mathematics Subject Classification

  • 80A22 49K20 49N45


  • inverse problem, bio-heat-equation, laser thermotherapy




We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic heat source inverse problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement.

Appeared in

  • J. Differential Equations, 266 (2019), pp. 7525--7544.

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