Approximation schemes for viscosity solutions of Hamilton-Jacobi equations
نویسندگان
چکیده
منابع مشابه
Viscosity Solutions of Hamilton-Jacobi Equations
Problems involving Hamilton-Jacobi equations-which we take to be either of the stationary form H(x, u, Du) = 0 or of the evolution form u, + H(x, t, u, Du) = 0, where Du is the spatial gradient of u-arise in many contexts. Classical analysis of associated problems under boundary and/or initial conditions by the method of characteristics is limited to local considerations owing to the crossing o...
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A theory of viscosity solutions in metric spaces based on local slopes was initiated in [39]. In this manuscript we deepen the study of [39] and present a more complete account of the theory of metric viscosity solutions of Hamilton–Jacobi equations. Several comparison and existence results are proved and the main techniques for such metric viscosity solutions are illustrated.
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We define viscosity solutions for the Hamilton–Jacobi equation φt = v(x, t)H(∇φ) in RN × (0,∞) where v is positive and bounded measurable and H is non-negative and Lipschitz continuous. Under certain assumptions, we establish the existence and uniqueness of Lipschitz continuous viscosity solutions. The uniqueness result holds in particular for those v which are independent of t and piecewise co...
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A new concept of viscosity solutions, namely, the Hausdorff continuous viscosity solution for the Hamilton-Jacobi equation is defined and investigated. It is shown that the main ideas within the classical theory of continuous viscosity solutions can be extended to the wider space of Hausdorff continuous functions while also generalizing some of the existing concepts of discontinuous solutions.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1985
ISSN: 0022-0396
DOI: 10.1016/0022-0396(85)90136-6