| Abstract: |
| Reaction-diffusion equations / systems appear in many applications.
Often the coefficients or the nonlinearity itself is unknown and for the sake of generality one aims for a non-parametric form of the nonlinearity.
In this talk we consider inverse problems of recovering potentials and/or state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variables either at a fixed finite time (census-type data) or a time trace of their values at a fixed point on the boundary of the spatial domain.
The basic idea of an iteration scheme that can be applied in many cases relies on projecting the data onto the observation manifold. We can then express those parts of the differential operators in the PDE that are tangential to this manifold via the data; and those parts that are perpendicular to the manifold via PDE solutions.
This leads to a fixed point formulation and thus to a reconstructive method and we shall demonstrate its effectiveness by several illustrative examples. |
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