Blow-up Dynamics of Higher Dimensional Klein-Gordon Equation with Nonminimal Coupling in Subcritical Case
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Abstract
The aim of this present work is to study the blow-up dynamics and lifespan
estimate for solution to higher dimensional Klein-Gordon Equation in subcritical case, in which
1 < p < psc. We construct the equation of motion from the Lagrangian of Klein-Gordon with
non-minimal coupling, where the coupling interaction of the scalar field is proportional to the
scalar curvature of the spacetime. The equation of motion has the form like nonlinear damped
wave equation with mass. The novelty of this work is the time dependent of nonlinear term. We
use test function method to proof the lifespan estimate.
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How to Cite
Wijayanto, M., Akbar, F., & Gunara, B. (2022). Blow-up Dynamics of Higher Dimensional Klein-Gordon Equation with Nonminimal Coupling in Subcritical Case. Indonesian Journal of Physics, 33(1), 45 - 50. https://doi.org/10.5614/itb.ijp.2022.33.1.5
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References
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[6] Lai N A, Schiavone N M, and Takamura H. Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type Lemma. Journal of Differential Equations, 269, 11575–11620, 2020.
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[2] D'Abicco M, Girardi D, Reissig M. A scale of critical exponents for semilinear waves with time-dependent damping and mass terms. Nonlinear Analysis, 179, 15-40, 2019.
[3] Ikeda M, Tu Z, Wakasa K. Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass. Evolution Equations and Control Theory, 11 (2) : 515-536, 2022.
[4] Iqbal M, Akbar F T, and Gunara B E. Local existence of scalar wave equation on the Robertson-Walker universe as a background with k = 0. Journal of Physics: Conference Series 1204 (2019): 012131, 2019.
[5] Lai N A, Schiavone N M, and Takamura H. Wave-like blow-up for semilinear wave equations with scattering damping and negative mass. in "New Tools for Nonlinear PDEs and Application, Trends in Mathematics", (eds. D'Abbicco, M., Ebert, M., Georgiev, V., and Ozawa, T.), Birkha ̈user, 168, 217–240, 2019.
[6] Lai N A, Schiavone N M, and Takamura H. Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type Lemma. Journal of Differential Equations, 269, 11575–11620, 2020.
[7] Palmieri A, and Tu Z. Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity. Journal of Mathematical Analysis and Aplications, doi:10.1016/j.jmaa.2018.10.015, 2019.
[8] Wijayanto M P, Akbar F T, Gunara B E. Local Existence of Classical Solutions to Scalar Field Equation on Spatially Compact Spacetime as a Background. Journal of Physics: Conference Series, 1949. doi:10.1088/1742-6596/1949/1/012011, 2019