Penalization via global functionals of optimal-control problems for\n 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

paper · pdf · doi:10.48550/arxiv.1910.10050

openalex publication_date 2019/10/22 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

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

Citations

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

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