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- W4316038370 abstract "We are concerned with the existence and multiplicity of nontrivial time periodic viscosity solutions to∂tw(x,t)+H(x,∂xw(x,t),w(x,t))=0,(x,t)∈S×[0,+∞), where S is the unit circle and H=H(x,p,u) satisfies Tonelli conditions with respect to the argument p and is strictly decreasing in the argument u. We also study the long time behavior of viscosity solutions of the Cauchy problem for the above contact Hamilton-Jacobi equation. It is shown that for a class of initial data the corresponding viscosity solutions converge to asymptotic time periodic viscosity solutions. As an application of the existence result we analyze a bifurcation phenomenon for ∂tw(x,t)+H(x,∂xw(x,t),λw(x,t))=0 where λ is a parameter. Nous nous intéressons à l'existence et à la multiplicité de solutions de viscosité périodique temporelles non triviales à∂tw(x,t)+H(x,∂xw(x,t),w(x,t))=0,(x,t)∈S×[0,+∞), où S est le cercle unité et H=H(x,p,u) satisfait aux conditions de Tonelli en p et est strictement décroissant en u. Nous étudions également le comportement à long terme des solutions de viscosité du problè me de Cauchy pour l'équation de Hamilton-Jacobi de contact ci-dessus. Il est montré que pour une classe de données initiales, les solutions de viscosité correspondantes convergent vers des solutions de viscosité périodique asymptotique en temps. En tant qu'application du résultat d'existence, nous analysons un phénomè ne de bifurcation pour∂tw(x,t)+H(x,∂xw(x,t),λw(x,t))=0, où λ est un paramètre." @default.
- W4316038370 created "2023-01-14" @default.
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- W4316038370 date "2023-03-01" @default.
- W4316038370 modified "2023-10-15" @default.
- W4316038370 title "Time periodic solutions of Hamilton-Jacobi equations with autonomous Hamiltonian on the circle" @default.
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- W4316038370 doi "https://doi.org/10.1016/j.matpur.2023.01.002" @default.
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