2015/03/23 by Élder J. Villamizar‐Roa, Villamizar-Roa, Elder J., Diego A. Rueda-Gómez +1
Computer Science · Engineering · Mathematics · #35A01 #35A02 #35C06 #35Q55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1503.06734
openalex publication_date 2015/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study a boundary control problem associated to the\nstationary Rayleigh-B 'enard-Marangoni (RBM) system in presence of controls for\nthe velocity and the temperature on parts of the boundary. We analyze the\nexistence, uniqueness and regularity of weak solutions for the stationary RBM\nsystem in polyhedral domains of \ℝ3, and then, we prove the\nexistence of the optimal solution. By using the Theorem of Lagrange\nmultipliers, we derive an optimality system. We also give a second-order\nsufficient optimality condition and we establish a result of uniqueness of the\noptimal solution.\n