Non-diffusive large time behaviour for a degenerate viscous Hamilton-Jacobi equation
Comportamento di grande durata non diffusivo per un'equazione di Hamilton-Jacobi viscosa degenerata
Résumé
The convergence to non-diffusive self-similar solutions is investigated for non-negative solutions to the Cauchy problem ∂ t u = ∆ p u + |∇u| q when the initial data converge to zero at infinity. Sufficient conditions on the exponents p > 2 and q > 1 are given that guarantee that the diffusion becomes negligible for large times and the L ∞-norm of u(t) converges to a positive value as t → ∞.
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