Optimal control of a convective-diffusive fluid problem. (English) Zbl 0828.76066

Lenhart, Suzanne

Math. Models Methods Appl. Sci. 5, No. 2, 225-237 (1995).

Summary: We consider optimal control of a parabolic differential equation modeling one-dimensional fluid flow through a soil-packed tube in which a contaminant is initially distributed. A fluid is pumped through the tube to remove the contaminant. The convective velocity due to the fluid pumping is the nonlinear control action. The goal is to minimize a performance criterion which is a combination of the total contaminant at the final time and the cost of the control. The optimal control is characterized by an optimality system.

MSC:

76M30	Variational methods applied to problems in fluid mechanics
76R99	Diffusion and convection
49J20	Existence theories for optimal control problems involving partial differential equations

Keywords:

parabolic differential equation; soil-packed tube; contaminant; nonlinear control action; performance criterion; optimality system