Amal Attouchi

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We investigate the boundedness and large time behavior of solutions of the Cauchy–Dirichlet problem for the onedimensional degenerate parabolic equation with gradient nonlinearity: ut = (|ux|ux)x + |ux| in (0,∞) × (0, 1), q > p > 2. We prove that: either ux blows up in finite time, or u is global and converges in W 1,∞(0, 1) to the unique steady state. This(More)
In this article, we are interested in the Dirichlet problem for parabolic viscous Hamilton-Jacobi Equations. It is well-known that the gradient of the solution may blow up in finite time on the boundary of the domain, preventing a classical extension of the solution past this singularity. This behavior comes from the fact that one cannot prescribe the(More)
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