Simultaneous determination of different class of parameters for a diffusion equation from a single measurement

Abstract

Abstract This article is devoted to the simultaneous resolution of several inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single boundary measurement. Namely, we consider the simultaneous unique determination of several class of coefficients, some internal sources (a source term and an initial condition) and the fractional order in a diffusion equation from a single boundary measurement. Our problem can be formulated as the simultaneous determination of information about a diffusion process (velocity field, density of the medium) and of the source of diffusion. We consider this problems in the context of a classical diffusion process described by a convection–diffusion equation as well as an anomalous diffusion phenomena described by a time fractional diffusion equation.