A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivative-type in the generalized Einstein-de Sitter spacetime
arXiv:2101.12626 · doi:10.3934/cpaa.2021127
Abstract
In this paper, we establish blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime with nonlinearity of derivative type. Our approach is based on the integral representation formula for the solution to the corresponding linear problem in the one-dimensional case, that we will determine through Yagdjian's Integral Transform approach. As upper bound for the exponent of the nonlinear term, we discover a Glassey-type exponent which depends both on the space dimension and on the Lorentzian metric in the generalized Einstein-de Sitter spacetime.
References in corpus (10)
- Spatio-Temporal Analysis of On Demand Transit: A Case Study of Belleville, Canada
- Fundamental Solutions for the Klein-Gordon Equation in de Sitter Spacetime
- The semilinear Euler-Poisson-Darboux equation: a case of wave with critical dissipation
- On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime
- Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
- A blow-up result for a generalized Tricomi equation with nonlinearity of derivative type
- Lifespan estimates for local solutions to the semilinear wave equation in Einstein-de Sitter spacetime
- Fundamental Solutions for Hyperbolic Operators with Variable Coefficients
- Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type
- New blow-up result for the weakly coupled wave equations with a scale-invariant damping and time derivative nonlinearity
Cited by in corpus (5)
- On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity
- Fundamental solutions for the Dirac equation in curved spacetime and generalized Euler-Poisson-Darboux equation
- A blow-up result for a Nakao-type weakly coupled system with nonlinearities of derivative-type
- Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type
- On a semilinear wave equation in anti-de Sitter spacetime: the critical case