Global propagation of analyticity and unique continuation for semilinear conservative PDEs
[Propagation globale de l’analyticité et prolongement unique pour des équations semilinéaires conservatives]
Camille Laurent1 ; Cristóbal Loyola2
1Laboratoire de Mathématiques de Reims (LMR)-UMR 9008, U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, 51687 REIMS cedex 2, France
2Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 Place Jussieu, 75005 Paris, France
Journées équations aux dérivées partielles (2025), Exposé no. 3, 18 p.

We review some recent results in which we develop a new method for proving global unique continuation for some conservative PDEs. The main tool is to prove some global propagation of analyticity. We first present some known results on the subject. Then, we sketch the abstract method we use, which relies on some finite determining mode property. We give applications to semilinear wave, plates and Schrödinger equation.

Nous passons en revue des résultats récents où nous développons une nouvelle méthode pour obtenir des résultats de prolongement unique pour des EDP conservatives. L’outil principal est une preuve de propagation globale de l’analyticité. Nous présentons des résultats connus sur le sujet. Ensuite, nous donnons une esquisse de la méthode abstraite que nous utilisons, qui repose sur une reconstruction à partir d’un nombre fini de modes. Nous donnons des applications aux ondes non linéaires, aux plaques non linéaires et à l’équation de Schrödinger non linéaire.

Publié le :
DOI : 10.5802/jedp.694
Classification : 35A20, 35B60, 93B07, 35L71, 35L75, 35Q55
Keywords: propagation of analyticity, unique continuation, semilinear wave equation, semilinear plate equation, semilinear Schrödinger equation

Camille Laurent  1   ; Cristóbal Loyola  2

1 Laboratoire de Mathématiques de Reims (LMR)-UMR 9008, U.F.R. Sciences Exactes et Naturelles, Moulin de la Housse - BP 1039, 51687 REIMS cedex 2, France
2 Laboratoire Jacques-Louis Lions, Sorbonne Université, 4 Place Jussieu, 75005 Paris, France 
Camille Laurent; Cristóbal Loyola. Global propagation of analyticity and unique continuation for semilinear conservative PDEs. Journées équations aux dérivées partielles (2025), Exposé no. 3, 18 p.. doi: 10.5802/jedp.694
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