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Parameter estimation in moving boundary problems. (English) Zbl 0656.65106

We describe an approximation scheme which can be used to estimate unknown parameters in moving boundary problems. The model equations we consider are fairly general nonlinear diffusion/reaction equations of one spatial variable. Here we give conditions on the parameter sets and model equations under which we can prove that the estimates obtained using the approximations will converge to best-fit parameters for the original model equations. We conclude with a numerical example.

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
35K57 Reaction-diffusion equations
35R30 Inverse problems for PDEs
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References:

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