On-line detecting heat source of a nonlinear heat conduction equation by a differential algebraic equation method

We consider an inverse problem for detecting an unknown time-dependent heat source in real-time for a nonlinear heat conduction equation, with the aid of an extra measurement of temperature at an internal point. After a finite difference discretization of governing equation into ordinary differential equations, we recast them and the measured data as a set of differential algebraic equations (DAEs), which is a novel view of the inverse heat source problem. Then we solve the resultant DAEs by a GL(n,R) Lie-group method, which can be used as an on-line estimator to detect unknown heat source of nonlinear heat conduction equation, by using only a real-time measurement of internal temperature under a randomly noisy disturbance. The estimated results obtained by the novel Lie-group differential algebraic equations (LGDAE) method are quite promising and robust enough against large random noises.