Determination of a Time-Varying Point Source in Cauchy Problems for the Convection–Diffusion Equation

Abstract

In this paper, we suggest a method for recovering the unknown time-dependent strength of a contaminant concentration source from measurements of the concentration inside an unbounded domain. This problem is formulated as a Cauchy parabolic inverse problem. For its efficient numerical processing, the problem is solved by reduction of the Cauchy problem to a Dirichet one on a bounded domain using the method of the fundamental (potential) solutions in combination with an adjoint equation technique. A numerical solution to this approach is explained. Next, by choosing the source strength in the form of a finite series of shape functions with unknown constant coefficients and using a linear-square method, the term concentration source is estimated. Computational simulations using model examples from water pollution are discussed.

Keywords

• parabolic Cauchy problem
• boundary conditions
• dispersion modeling
• point source
• inverse problem
• adjoint equation