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- W2069854767 abstract "We study the Dirichlet problem for viscous Hamilton–Jacobi equations. Despite this type of equations seems to be uniformly elliptic, loss of boundary conditions may occur because of the strong nonlinearity of the first-order part and therefore the Dirichlet boundary condition has to be understood in the sense of viscosity solutions theory. Under natural assumptions on the initial and boundary data, we prove a Strong Comparison Result which allows us to obtain the existence and the uniqueness of a continuous solution which is defined globally in time. Nous étudions le problème de Dirichlet pour des équations non linéaires paraboliques de type Hamilton–Jacobi avec viscosité. Bien que ces équations semblent uniformément elliptiques, des pertes de conditions aux limites peuvent se produire à cause de la forte non-linéarité du terme du premier ordre et on doit utiliser la notion de condition aux limites généralisée au sens de la théorie des solutions de viscosité. Sous des hypothèses naturelles sur la donnée initiale et la condition au bord, nous démontrons un résultat de comparaison fort qui nous permet d'obtenir l'existence et l'unicité d'une solution de viscosité continue qui est définie pour tous temps." @default.
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- W2069854767 date "2004-01-01" @default.
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- W2069854767 title "On the generalized Dirichlet problem for viscous Hamilton–Jacobi equations" @default.
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- W2069854767 doi "https://doi.org/10.1016/s0021-7824(03)00070-9" @default.
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