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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

For fixed ρ = ρ(x, t), we consider the solution u(f) to  $$\begin{array}{*{20}{c}} {u''(x,t) + Au(x,t)\quad = \quad f(x)\rho (x,t),\quad x \in \Omega ,t > 0}\\ {u(x,0)\quad = \quad u'(x,0) = 0,\quad x \in \Omega ,}\\ {{B_j}u(x,t)\quad = \quad 0,\quad x \notin \partial \Omega ,t > 0,1 \le j \le m,} \end{array} $$  where $u' = \frac{{\partial u}}{{\partial t}},u'' = \frac{{{\partial ^2}u}}{{\partial {t^2}}},\Omega \subset {R^r},r \ge 1$ is a bounded domain with smooth boundary, A is a uniformly symmetric elliptic differential operator of order 2m with t-independent smooth coefficients, B j , 1 ≤ j ≤ m, are t-independent boundary differential operators such that the system {A, B j }1≤j≤m is well-posed. Let {C j }1≤j≤m be complementary boundary differential operators of {B j }1≤j≤m . We consider a multidimensional linear inverse problem: for given Γ ⊂ ∂Ω, T > 0 and n ∈ {1, ..., m}, determine f(x), x ∈ Ω from C j u(f)(x, t), x ∈ Г, 0 > t > T, 1 ≤ j ≤ n.

Reconstruction of Source Terms in Evolution Equations by Exact Controllability