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

Let $\Omega\subset \mathbb{R}^N$, $N=1,2,3$, be an open bounded and connectedset with continuous piecewise $\mathrm{C}^{\infty}$ boundary. Here we deal withalmost periodic distributions of the form $u(t,x)=\sum_{n=0}^{+\infty} c_nS_n(x) \mathrm{e}^{i \lambda_n t}$ where $(c_n)_{n\in \mathbb{N}}\subset\mathbb{C}$ belong to the space of slowing growing sequences $s^\prime$, and$(\lambda_n^2)_{n\in\mathbb{N}}\subset \mathbb{R}$ and$(S_n)_{n\in\mathbb{N}}\subset \mathrm{H}_0^{1}(\Omega)$ are respectively theeigenvalues and eigenvectors of the Laplacian. Given $\omega\subset\Omega$, weprove that there exists $T_{max}(\Omega,\omega)>0$ depending only on $\Omega$and $\omega$ such that if $T>T_{max}(\Omega,\omega)$ and $u|_{\omega\times]-T,T[}=0$, then $u\equiv 0$. Using this result we prove a unique continuationproperty for the wave equation.

Uniqueness result for Almost Periodic Distributions depending on time and space and an application to the unique continuation for the wave equation