Article detail · 2002
REVERSE CONVOLUTION INEQUALITIES AND APPLICATIONS TO INVERSE HEAT SOURCE PROBLEMS
- Year
- 2002
- Type
- article
Abstract
OpenAlex · English
ABSTRACT. We introduce reverse convolution inequalities obtained recently and at the same time, we give new type reverse convolution inequalities and their important applications to inverse source problems. We consider the inverse problem of determining f(t), 0 < t < T, in the heat source of the heat equation ∂tu(x, t) = ∆u(x, t) + f(t)ϕ(x), x ∈ R n, t> 0 from the observation u(x0, t), 0 < t < T, at a remote point x0 away from the support of ϕ. Under an a priori assumption that f changes the signs at most N-times, we give a conditional stability of Hölder type, as an example of applications.
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66 citations
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18 publications in the local catalog that cite this work (OpenAlex reference match; not the full global list).
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