Null controllability for the semilinear heat equation in a non-smooth domain

Ali-Ziane, Tarik; Ferhoune, Zahia; Zair, Ouahiba

doi:10.1016/j.crma.2015.01.005

Partial differential equations

Null controllability for the semilinear heat equation in a non-smooth domain
[Nulle contrôlabilité de l'équation de la chaleur semilinéaire dans un domaine non régulier]

Présenté par : Gilles Lebeau

Ali-Ziane, Tarik ¹ ; Ferhoune, Zahia ¹ ; Zair, Ouahiba ¹

¹ Laboratoire AMNEDP, Faculté de Mathématiques, USTHB, BP 32, El-Alia, 16111 Alger, Algeria

Comptes Rendus. Mathématique, Tome 353 (2015) no. 3, pp. 229-234.

Résumé
Abstract

Dans ce travail, on donne un résultat de nulle contrôlabilité pour l'équation de la chaleur semi-linéaire dans un domaine borné de $R^{2}$ , polygonal ou fissuré. On suppose que la non-linearité croît moins vite que $| s | \log^{3 / 2} (1 + | s |)$ quand $| s | \to \infty$ , et on démontre le résultat par le théorème du point fixe de Schauder.

In this work we give a null-controllability result for the semi-linear heat equation in a polygonal or cracked bounded domain of $R^{2}$ . We suppose that the nonlinearity grows slower than $| s | \log^{3 / 2} (1 + | s |)$ as $| s | \to \infty$ and then we prove our result by using Schauder's fixed point theorem.

Reçu le : 2014-10-20
Accepté le : 2015-01-19
Publié le : 2015-01-29

DOI : 10.1016/j.crma.2015.01.005

Affiliations des auteurs :

Ali-Ziane, Tarik ¹ ; Ferhoune, Zahia ¹ ; Zair, Ouahiba ¹

¹ Laboratoire AMNEDP, Faculté de Mathématiques, USTHB, BP 32, El-Alia, 16111 Alger, Algeria

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     title = {Null controllability for the semilinear heat equation in a non-smooth domain},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {229--234},
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     doi = {10.1016/j.crma.2015.01.005},
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     url = {http://archive.numdam.org/articles/10.1016/j.crma.2015.01.005/}
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Ali-Ziane, Tarik; Ferhoune, Zahia; Zair, Ouahiba. Null controllability for the semilinear heat equation in a non-smooth domain. Comptes Rendus. Mathématique, Tome 353 (2015) no. 3, pp. 229-234. doi : 10.1016/j.crma.2015.01.005. http://archive.numdam.org/articles/10.1016/j.crma.2015.01.005/

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