Journal article
Nonexistence result for the generalized Tricomi equation with the scale-invariant damping, mass term and time derivative nonlinearity


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Author list: Ben Hassen, Moahmed Fahmi | Hamouda, Makram; * | Hamza, Mohamed Ali | Teka, Hanen Khaled
Publisher: IOS Press
Publication year: 2021
Journal: Asymptotic Analysis
Volume number: Pre-press
Issue number: Pre-press
Start page: 1
End page: 21
Number of 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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Last updated on 2021-08-11 at 12:04

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