Singular optimal control of a 1-D parabolic-hyperbolic degenerate equation

Singular Optimal Control of a 1-D Parabolic-Hyperbolic Degenerate Equation

In this paper, we consider the controllability of a strongly degenerate parabolic equation with a degenerate one-order transport term. Despite the strong degeneracy, we prove a result of well-posedness and null controllability with a Dirichlet boundary control that acts on the degenerate part of the boundary. Then, we study the uniform controllability in the vanishing viscosity limit and prove ...

Optimal control and Riccati equation for a degenerate parabolic system

In this paper, we consider a stabilization problem for a fluid flow. For a perturbation of the velocity of an incoming flow on a flat plate, the laminar-to-turbulent transition location varies. We want to stabilize it by a suction velocity trough the plate. The linearization of the nonlinear model around a steady state solution leads to a linear degenerate parabolic equation. We look for a suct...

Optimal control of a semilinear parabolic equation with singular arcs

This paper develops a theory of singular arc, and the corresponding second order necessary and sufficient conditions, for the optimal control of a semilinear parabolic equation with scalar control applied on the r.h.s. We obtain in particular an extension of Kelley’s condition, and the characterization of a quadratic growth property for a weak norm.

Optimal Control for Degenerate Parabolic Equations

This paper considers the optimal control of a degenerate parabolic partial differential equation governing a di usive population with logistic growth terms. Assuming this population causes damage to forest and agricultural land, the optimal control is the trapping rate and the cost functional is a combination of the damage and trapping costs. We prove existence, uniqueness, and regularity resul...

Convergence of Singular Limitsfor Multi - D Semilinear Hyperbolic Systemsto Parabolic