TY - JOUR
T1 - Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities
AU - Palmieri, Alessandro
AU - Takamura, Hiroyuki
N1 - Funding Information:
The first author is member of the Gruppo Nazionale per L’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Instituto Nazionale di Alta Matematica (INdAM). This paper was written partially during the stay of the first author at Tohoku University in 2018. He would like to thank the Mathematical Department of Tohoku University for the hospitality and the excellent working conditions during this period. The first author is supported by University of Pisa , Project PRA 2018 49 . The second author is partially supported by the Grant-in-Aid for Scientific Research (B) (No. 18H01132 ). Both authors thank the anonymous referee for carefully reading the manuscript and for his/her suggestion that helped to simplify the proof of Lemma 2.2 .
Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/10
Y1 - 2019/10
N2 - In this work we study the blow-up of solutions of a weakly coupled system of damped semilinear wave equations in the scattering case with power nonlinearities. We apply an iteration method to study both the subcritical case and the critical case. In the subcritical case our approach is based on lower bounds for the space averages of the components of local solutions. In the critical case we use the slicing method and a couple of auxiliary functions, recently introduced by Wakasa-Yordanov, Wakasa–Yordanov, to modify the definition of the functionals with the introduction of weight terms. In particular, we find as critical curve for the pair (p,q) of the exponents in the nonlinear terms the same one as for the weakly coupled system of semilinear wave equations with power nonlinearities.
AB - In this work we study the blow-up of solutions of a weakly coupled system of damped semilinear wave equations in the scattering case with power nonlinearities. We apply an iteration method to study both the subcritical case and the critical case. In the subcritical case our approach is based on lower bounds for the space averages of the components of local solutions. In the critical case we use the slicing method and a couple of auxiliary functions, recently introduced by Wakasa-Yordanov, Wakasa–Yordanov, to modify the definition of the functionals with the introduction of weight terms. In particular, we find as critical curve for the pair (p,q) of the exponents in the nonlinear terms the same one as for the weakly coupled system of semilinear wave equations with power nonlinearities.
KW - Blow-up
KW - Scattering producing damping
KW - Semilinear weakly coupled system
UR - http://www.scopus.com/inward/record.url?scp=85067835899&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85067835899&partnerID=8YFLogxK
U2 - 10.1016/j.na.2019.06.016
DO - 10.1016/j.na.2019.06.016
M3 - Article
AN - SCOPUS:85067835899
SN - 0362-546X
VL - 187
SP - 467
EP - 492
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -