On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation

by   Barbara Kaltenbacher, et al.

This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity a(x) and the nonlinear reaction term f(u) in a reaction-diffusion equation from overposed data. These measurements can consist of: the value of two different solution measurements taken at a later time T; time-trace profiles from two solutions; or both final time and time-trace measurements from a single forwards solve data run. We prove both uniqueness results and the convergence of iteration schemes designed to recover these coefficients. The last section of the paper shows numerical reconstructions based on these algorithms.


page 1

page 2

page 3

page 4


The Inverse Problem of Reconstructing Reaction-Diffusion Systems

This paper considers the inverse problem of recovering state-dependent s...

On the simultanenous identification of two space dependent coefficients in a quasilinear wave equation

This paper considers the Westervelt equation, one of the most widely use...

On uniqueness and reconstruction of a nonlinear diffusion term in a parabolic equation

The problem of recovering coefficients in a diffusion equation is one of...

On an inverse problem of nonlinear imaging with fractional damping

This paper considers the attenuated Westervelt equation in pressure form...

Modeling Firn Density through Spatially Varying Smoothed Arrhenius Regression

Scientists use firn (compacted snow) density models as a function of dep...

Parameter and density estimation from real-world traffic data: A kinetic compartmental approach

The main motivation of this work is to assess the validity of a LWR traf...

Please sign up or login with your details

Forgot password? Click here to reset