Blow-up of a nonlocal $p$-Laplacian evolution equation with critical initial energy

Yang Liu; Pengju Lv; Chaojiu Da

doi:10.4064/ap3807-1-2016

Geodesic

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Blow-up of a nonlocal $p$-Laplacian evolution equation with critical initial energy

Yang Liu ¹ ; Pengju Lv ² ; Chaojiu Da ¹

¹ College of Mathematics and Computer Science Northwest University for Nationalities 730124 Lanzhou, People’s Republic of China
² Department of Medical Informatics Harbin Medical University 163319 Daqing, People’s Republic of China

Annales Polonici Mathematici, Tome 117 (2016) no. 1, pp. 89-99.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

This paper is concerned with the initial boundary value problem for a nonlocal $p$-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

DOI : 10.4064/ap3807-1-2016

Keywords: paper concerned initial boundary value problem nonlocal p laplacian evolution equation critical initial energy framework energy method construct unstable set establish its invariance finally finite time blow up solutions derived combination unstable set concavity method

Affiliations des auteurs :

Yang Liu ¹ ; Pengju Lv ² ; Chaojiu Da ¹

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Yang Liu; Pengju Lv; Chaojiu Da. Blow-up of a nonlocal $p$-Laplacian evolution equation with critical initial energy. Annales Polonici Mathematici, Tome 117 (2016) no. 1, pp. 89-99. doi : 10.4064/ap3807-1-2016. http://geodesic.mathdoc.fr/articles/10.4064/ap3807-1-2016/

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