2019/11/07 by Sheetal Dharmatti, Dharmatti, Sheetal, Mahendranath PL N +1 · 1 citation
Computer Science · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.1911.02811
openalex publication_date 2019/11/07 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In this paper we study optimal control problem for non local\nCahn-Hilliard-Brinkman system which models phase separation of binary fluids in\nporous media. We consider the system in two dimensional bounded domain with\nregular potential. We extend recently proved existence of weak solution results\nfor such a system and prove the existence of strong solution under certain\nassumptions on the forcing term and initial datum. Further using our regularity\nresults, we study the tracking type optimal control problem. We prove the\nexistence of an optimal control and establish the first order optimality\ncondition. Lastly, we characterize optimal control in terms of the solution of\ncorresponding adjoint system. The existence of solution for the adjoint system\nis also established.\n