Philippe Laurencot, Univ Toulouse, France
Non-diffusive large time behaviour for a degenerate viscous Hamilton-Jacobi equation(joint work with Jean-Philippe Bartier and Juan Luis Vazquez)
We investigate the large time behaviour of a diffusive Hamilton-Jacobi equation involving a quasilinear degenerate diffusion (p-Laplacian) and a nonlinear reaction term depending solely on the gradient, the latter being either an absorption term or a source term. Assuming the reaction term to be the euclidean norm of the gradient to the power q, a range of the parameters p and q is identified for which the influence of the diffusion is negligible for large times. Convergence to self-similar solutions of the Hamilton-Jacobi equation (without diffusion) is then established.
TUESDAY, May 20, 2008