## Analysis of a quasi-reversibility method for a terminal value quasi-linear parabolic problem with measurements. (arXiv:1803.04641v2 [math.NA] UPDATED)

This paper presents a modified quasi-reversibility method for computing the
exponentially unstable solution of a nonlocal terminal-boundary value parabolic
problem with noisy data. Based on data measurements, we perturb the problem by
the so-called filter regularized operator to design an approximate problem.
Different from recently developed approaches that consist in the conventional
spectral methods, we analyze this new approximation in a variational framework,
where the finite element method can be applied. To see the whole skeleton of
this method, our main results lie in the analysis of a semi-linear case and we
discuss some generalizations where this analysis can be adapted. As is
omnipresent in many physical processes, there is likely a myriad of models
derived from this simpler case, such as source localization problems for brain
tumors and heat conduction problems with nonlinear sinks in nuclear science.
With respect to each noise level, we benefit from the Faedo-Galerkin meth查看全文