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Local and global existence of solutions to scalar equations on spatially flat universe as a background with non-minimal coupling

Akbar, Fiki T and Gunara, Bobby E and Iqbal, Muhammad and Susanto, Hadi (2019) 'Local and global existence of solutions to scalar equations on spatially flat universe as a background with non-minimal coupling.' Advances in Theoretical and Mathematical Physics, 23 (1). pp. 1-26. ISSN 1095-0753

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Abstract

We prove the wellposedness of scalar wave equations on spatially at universe as a background with nonminimal coupling with the scalar potential turned on by introducing the k-order linear energy and the corresponding energy norm. In the local case, we show that both the k-order linear energy and the energy norm are bounded for finite time with initial data in Hk+1 x Hk. Whereas in the global case, we have to add three assumptions related to the nonminimal coupling constant, the scale factor of spacetimes, and the form of the scalar potential that has to be a polynomial with a small positive parameter. Then, we show that the solution does globally exist with a particular decay estimate that depends on the scale factor of the spacetimes. Finally, we provide some physical models that support our general setup.

Item Type: Article
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 18 Nov 2019 16:26
Last Modified: 23 Sep 2022 19:35
URI: http://repository.essex.ac.uk/id/eprint/25772

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