Stabilization for the semilinear wave equation with geometric control condition
type: Dataset
description: In this article, we prove the exponential stabilization of the semilinear wave equation with a damping effective in a zone satisfying the geometric control condition only. The nonlinearity is assumed to be subcritical, defocusing and analytic. The main novelty compared to previous results, is the proof of a unique continuation result in large time for some undamped equation. The idea is to use an asymptotic smoothing effect proved by Hale and Raugel in the context of dynamical systems. Then, once the analyticity in time is proved, we apply a unique continuation result with partial analyticity due to Robbiano, Zuily, Tataru and Hörmander. Some other consequences are also given for the controllability and the existence of a compact attractor.
issued: 2026-05-08T00:05:28.324035
language: en
modified: 2026-05-08T00:05:28.324039
contact point: Organization
  fn: CCSD
keyword: 35b40-35b60-35b65-35l71-93d20-35b41
keyword: analyticity
keyword: compact-attractor
keyword: damped-wave-equation
keyword: infoeu-reposemanticsarticle
keyword: journal-articles
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: stabilization
keyword: unique-continuation-property
landing page: 2157-5045

Stabilization for the semilinear wave equation with geometric control condition
type: Distribution
format: HTML
issued: 2026-05-08T00:05:28.329661
modified: 2026-05-08T00:05:28.312833
access URL: https://hal.science/hal-00696147

test_moissonnage_selune
type: Agent