Data fitting in partial differential algebraic equations: some academic and industrial applications

The paper introduces a numerical method to estimate parameters in systems of one-dimensional partial differential algebraic equations. Proceeding from given experimental data, i.e., observation times and measurements, the minimum least-squares distance of measured data from a fitting criterion is computed, which depends on the solution of the dynamical system. We present a typical black box approach that is easily implemented proceeding from some standard numerical analysis tools. Main emphasis of the paper is to present a couple of practical applications from industry and academia, to give an impression on the complexity of real-life systems of partial differential equations. The domains of application are pharmaceutics, geology, mechanical engineering, chemical engineering, food engineering, and electrical engineering.