5 papers
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…
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…
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…
Large time behavior for a viscous Hamilton-Jacobi equation with Neumann boudary condition
Said Benachour, Simona Dabuleanu
We prove the existence and the uniqueness of strong solutions for the viscous Hamilton-Jacobi Equation with Neumann boundary condition and initial data a continious function. Then,…
Decay Estimates for a Viscous Hamilton-Jacobi Equation with Homogenious Dirichet Boundary Conditions
Said Benachour, Simona Dabuleanu-Hapca, Philippe Laurençot
Global classical solutions to the viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions are shown to converge to zero at the same speed as the linear heat…