Identification of the Heat Transfer Coefficient from Boundary Integral Data

We consider a second order parabolic equation and the well-posednessof inverse problems of recovering the heat transfercoefficients in Sobolev spaceswith the use of a collection of integrals of a solution over theboundary of a domain. Under certain conditions on the data, wedemonstrate that the existence of a unique local-in-time solution that depends continuouslyon the data. The method is constructive andallows us to provide some numerical methods of solution. The proof employsa priori estimates and the fixed point theorem.