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WELL-POSEDNESS ISSUES FOR SOME CRITICAL COUPLED NON-LINEAR KLEIN-GORDON EQUATIONS
Journal article   Open access  Peer reviewed

WELL-POSEDNESS ISSUES FOR SOME CRITICAL COUPLED NON-LINEAR KLEIN-GORDON EQUATIONS

Radhia Ghanmi, Tarek Saanouni and University Tunis El Manar, Faculty of Sciences of Tunis, 2092, Tunis, Tunisia
Communications on pure and applied analysis, Vol.18(2), pp.603-623
01/03/2019
DOI: https://doi.org/10.3934/cpaa.2019030

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
The initial value problem for some coupled non-linear wave equations is investigated. In the defocusing case, global well-posedness and ill-posedness results are obtained. In the focusing sign, the existence of global and non global solutions are discussed via the potential-well theory. Finally, strong instability of standing waves are established.
url
https://doi.org/10.3934/cpaa.2019030View
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