Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls

Hong Qiu; Jiongmin Yong

Displaying similar documents to “Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls”

Optimal control problems with upper semicontinuous Hamiltonians

Arkadiusz Misztela (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we give examples of value functions in Bolza problem that are not bilateral or viscosity solutions and an example of a smooth value function that is even not a classic solution (in particular, it can be neither the viscosity nor the bilateral solution) of Hamilton-Jacobi-Bellman equation with upper semicontinuous Hamiltonian. Good properties of value functions motivate us to introduce approximate solutions of equations with such type Hamiltonians. We show that the value...

GO++: A modular Lagrangian/Eulerian software for Hamilton Jacobi equations of geometric optics type

Jean-David Benamou, Philippe Hoch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.

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...

An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces

Piermarco Cannarsa, Giuseppe Da Prato (1988)

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

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We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.

An existence and uniqueness result for Hamilton-Jacobi equations in Hilbert spaces

Piermarco Cannarsa, Giuseppe Da Prato (1988)

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

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We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.

Concentration in the Nonlocal Fisher Equation: the Hamilton-Jacobi Limit

Benoît Perthame, Stephane Génieys (2010)

Mathematical Modelling of Natural Phenomena

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The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing instability and the interpretation refers to adaptive evolution. By analogy with other formalisms used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum of Dirac masses) will happen in the limit of small mutations. In the present work we study this asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation. We prove the convergence...

A note on the regularity of solutions of Hamilton-Jacobi equations with superlinear growth in the gradient variable

Pierre Cardaliaguet (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We investigate the regularity of solutions of first order Hamilton-Jacobi equation with super linear growth in the gradient variable. We show that the solutions are locally Hölder continuous with Hölder exponent depending only on the growth of the Hamiltonian. The proof relies on a reverse Hölder inequality.