Back to Search
Start Over
Blow-up of solutions for coupled wave equations with damping terms and derivative nonlinearities
- Source :
- AIMS Mathematics, Vol 9, Iss 10, Pp 26854-26876 (2024)
- Publication Year :
- 2024
- Publisher :
- AIMS Press, 2024.
-
Abstract
- This work was concerned with the weakly coupled system of semi-linear wave equations with time dependent speeds of propagation, damping terms, and derivative nonlinear terms in generalized Einstein-de Sitter space-time on $ \mathbb{R}^n $. Under certain assumptions about the indexes $ k_1, \, k_2 $, coefficients $ \mu_1, \, \mu_2 $, and nonlinearity exponents $ p, \, q $, applying the iteration technique, finite time blow-up of local solutions to the small initial value problem of the coupled system was investigated. Blow-up region and upper bound lifespan estimate of solutions to the problem were established. Compared with blow-up results in the previous literature, the new ingredient relied on that the blow-up region of solutions obtained in this work varies due to the influence of coefficients $ k_1, \, k_2 $.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 9
- Issue :
- 10
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.576ecf63f5ae405793773652706aaaa9
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.20241307?viewType=HTML