Reconstruction of a nonlinear source term in a semi-linear wave equation

• An inverse source problem associated with a semi-linear transport or one-way wave equation in one spatial dimension is considered. It is shown an analytic solution to the inverse problem can be given and furthermore, that this inverse problem of determination of a source function is ill-posed, and must be regularised. A novel regularisation scheme which combines least squares monotone approximation and mollification of the noisy data is used to provide this regularisation. Proof of convergence of this regularisation scheme of \emph{monotone smoothing} is given. Numerical solutions from the inverse problems are presented showing that the method is robust to noisy signals. The solution of this inverse problem is also shown to illustrate the behaviour of more complex problems from electromagnetism and nonlinear optics. The mathematical techniques that are developed are therefore applicable to other sets of nonlinear first order equations. The method is therefore model independent.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

Publikations- och innehållstyp

rap (ämneskategori)

vet (ämneskategori)