Article de journal
Nonexistence result for the generalized Tricomi equation with the scale-invariant damping, mass term and time derivative nonlinearity


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Liste des auteurs: Ben Hassen, Moahmed Fahmi | Hamouda, Makram; * | Hamza, Mohamed Ali | Teka, Hanen Khaled
Editeur: IOS Press
Année de publication: 2021
Journal: Asymptotic Analysis
Numéro du volume: Pre-press
Numéro de publication: Pre-press
Page d'accueil: 1
Dernière page: 21
Nombre de pages: 21
ISSN: 0921-7134
Web of Science ID:
PubMed-ID:
Scopus ID:
eISSN: 1875-8576


In this article, we consider the damped wave equation in the scale-invariant case with time-dependent speed of propagation, mass term and time derivative nonlinearity. More precisely, we study the blow-up of the solutions to the following equation: (E)utt−t2mΔu+μtut+ν2t2u=|ut|p,in RN×[1,∞), that we associate with small initial data. Assuming some assumptions on the mass and damping coefficients, ν and μ>0, respectively, we prove that blow-up region and the lifespan bound of the solution of (E) remain the same as the ones obtained for the case without mass, i.e. (E) with ν=0 which constitutes itself a shift of the dimension N by μ1+m compared to the problem without damping and mass. Finally, we think that the new bound for p is a serious candidate to the critical exponent which characterizes the threshold between the blow-up and the global existence regions.


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Dernière mise à jour le 2021-08-11 à 12:04