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Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation

Abstract : Convergence to a single steady state is shown for non-negative and radially symmetric solutions to a diffusive Hamilton-Jacobi equation with homogeneous Dirichlet boundary conditions, the diffusion being the $p$-Laplacian operator, $p\ge 2$, and the source term a power of the norm of the gradient of $u$. As a first step, the radially symmetric and non-increasing stationary solutions are characterized.
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Guy Barles, Philippe Laurençot, Christian Stinner. Convergence to steady states for radially symmetric solutions to a quasilinear degenerate diffusive Hamilton-Jacobi equation. Asymptotic Analysis, IOS Press, 2010, 67 (3-4), pp.229--250. ⟨10.3233/ASY-2010-0981⟩. ⟨hal-00401442⟩

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