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Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
Published online by Cambridge University Press: 05 June 2007
Abstract
In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_t+H(x,Du) = 0$ in ${\rm I}\!{\rm R}^n\times(0,T)$ where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 3 , July 2007 , pp. 484 - 502
- Copyright
- © EDP Sciences, SMAI, 2007
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