Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential

Abstract EN

A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements.

The evolution of the heat is given by a degenerate parabolic equation with singular potential.

This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field.

The mathematical model leads to a nonconvex minimization problem.

To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient).

Some numerical experiments are given.