English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the recovery of a source term $f(x,t)=p(x)q(t)$ for thenonhomogeneous heat equation in $\Omega\times (0,\infty)$ where $\Omega$ is abounded domain in $\mathbb{R}^2$ with smooth boundary $\partial\Omega$ fromoverposed lateral data on a sparse subset of $\partial\Omega\times(0,\infty)$.Specifically, we shall require a small finite number $N$ of measurement pointson $\partial\Omega$ and prove a uniqueness result; namely the recovery of thepair $(p,q)$ within a given class, by a judicious choice of $N=2$ points.Naturally, with this paucity of overposed data, the problem is severelyill-posed. Nevertheless we shall show that provided the data noise level islow, effective numerical reconstructions may be obtained.

On the identification of source term in the heat equation from sparse data