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The existence of a quaternary continuous classical optimal control controlled quaternary nonlinear elliptic equations.
- Source :
-
AIP Conference Proceedings . 2024, Vol. 3036 Issue 1, p1-6. 6p. - Publication Year :
- 2024
-
Abstract
- This paper is concerned by studding the continuous classical quaternary optimal control vector controlled with quaternary nonlinear elliptic partial differential equations. It deals with the mathematical formulation for the problem, including the quaternary nonlinear system, and the cost functional of the state - control vectors. The theorem of existence unique state quaternary vector solution of the weak form for the quaternary nonlinear elliptic system is stated and demonstrated through employing Minty-Browder theorem's, with given continuous classical quaternary control vector. The Lipschitz continuous operator between the continuous classical quaternary control vector and its conforming quaternary state vector solution is proved. State and proof for the theorem of existence a continuous classical quaternary optimal control vector of the constrained problem under suitable hypotheses through employing the Rellich–Kondrachov theorem [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 3036
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 176070398
- Full Text :
- https://doi.org/10.1063/5.0196161