Optimal control problem and viscosity solutions for the Vlasov equation in Yang–Mills charged Bianchi models
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Raoul Domingo Ayissi
und
Remy Magloire Etoua
Abstract
In 2005, Briani and Rampazzo [4], using the results of [10, 12, 13, 14], gave a density approach to Hamilton–Jacobi equations with t-measurable Hamiltonians. In this paper we firstly give more details and do more investigation on viscosity solutions for Hamilton–Jacobi equations. Then we show, using an important result of [4], the existence and uniqueness of viscosity solutions to the Vlasov relativistic equation in Yang–Mills charged Bianchi space times, with non zero mass. Thirdly, we clearly display, in the case of the Vlasov equation, the optimal control problem. To our knowledge, the method and techniques used here are original and thus, totally different from those used in [1, 5, 6, 8, 13, 15, 16] who have studied the same equation.
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© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Sparse signal recovery using a new class of random matrices
- The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman--Opdam theory on ℝd
- Generalized variational-like inclusion involving relaxed monotone operators
- A study on the product set-labeling of graphs
- Optimal control problem and viscosity solutions for the Vlasov equation in Yang–Mills charged Bianchi models
- Jaco-type graphs and black energy dissipation
Artikel in diesem Heft
- Frontmatter
- Sparse signal recovery using a new class of random matrices
- The positivity of the hypergeometric translation operators associated to the Cherednik operators and the Heckman--Opdam theory on ℝd
- Generalized variational-like inclusion involving relaxed monotone operators
- A study on the product set-labeling of graphs
- Optimal control problem and viscosity solutions for the Vlasov equation in Yang–Mills charged Bianchi models
- Jaco-type graphs and black energy dissipation
