Penalization via global functionals of optimal-control problems for dissipative evolution

2019/10/22 by Lorenzo Portinale, Portinale, Lorenzo, Ulisse Stefanelli +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.AP #math.OC

paper · pdf · doi:10.48550/arxiv.1910.10050

2 figures

arxiv created 2019/10/22 · openalex publication_date 2019/10/22 · arxiv updated 2019/10/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We consider an optimal control problem for an abstract nonlinear dissipative evolution equation. The differential constraint is penalized by augmenting the target functional by a nonnegative global-in-time functional which is null-minimized in the evolution equation is satisfied. Different variational settings are presented, leading to the convergence of the penalization method for gradient flows, noncyclic and semimonotone flows, doubly nonlinear evolutions, and GENERIC systems.

Citations

• Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

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