Displaying similar documents to “Perron's method and the method of relaxed limits for 'unbounded' PDE in Hilbert spaces”

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness...

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 Lincei. Matematica e Applicazioni

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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.

A Hamilton-Jacobi approach to junction problems and application to traffic flows

Cyril Imbert, Régis Monneau, Hasnaa Zidani (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to...

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

Similarity:

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.

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.