Displaying similar documents to “Hamilton-Jacobi equations for control problems of parabolic equations”

Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory

Guillaume Carlier, Rabah Tahraoui (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This article is devoted to the optimal control of state equations with memory of the form: x ˙ ( t ) = F ( x ( t ) , u ( t ) , ∫ 0 + ∞ A ( s ) x ( t - s ) d s ) , t > 0 , with initial conditions x ( 0 ) = x , x ( - s ) = z ( s ) , s > 0 . Denoting by y x , z , u the solution of the previous Cauchy problem and: v ( x , z ) : = inf u ∈ V { ∫ 0 + ∞ e - λ s L ( y x , z , u ( s ) , u ( s ) ) d s } where V is a class of admissible controls, we prove that v is the only viscosity solution of an Hamilton-Jacobi-Bellman equation...

Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations

Alessandra Cutrì, Francesca Da Lio (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form u t + H ( x , D u ) = 0 in I R n × ( 0 , T ) where the Hamiltonian may be noncoercive in the gradient As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.

Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities

Fabio Bagagiolo (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.

The vanishing viscosity method in infinite dimensions

Piermarco Cannarsa, Giuseppe Da Prato (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.

Homogenization of Hamilton-Jacobi equations in Carnot Groups

Bianca Stroffolini (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study an homogenization problem for Hamilton-Jacobi equations in the geometry of Carnot Groups. The tiling and the corresponding notion of periodicity are compatible with the dilatations of the Group and use the Lie bracket generating property.