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math.AP2008
Sharp Decay Estimates and Vanishing Viscosity for Diffusive Hamilton-Jacobi Equations
Said Benachour, Matania Ben-Artzi, Philippe Laurençot
Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equati…
math.AP2007
Asymptotic profiles of solutions to convection-diffusion equations
Said Benachour, Grzegorz Karch, Philippe Laurençot
The large time behavior of zero mass solutions to the Cauchy problem for a convection-diffusion equation. We provide conditions on the size and shape of the initial datum such that…
math.AP2007
Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations
Said Benachour, Grzegorz Karch, Philippe Laurençot
The large time behavior of solutions to Cauchy problem for viscous Hamilton-Jacobi equation is classified. The large time asymptotics are given by very singular self-similar soluti…