Non-diffusive large time behaviour for a degenerate viscous Hamilton-Jacobi equation

2008/07/29 by Laurençot, Philippe
#35B40 #35K55 #35K65 #49L25 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0807.4657

Abstract

The convergence to non-diffusive self-similar solutions is investigated for non-negative solutions to the Cauchy problem ∂_t u = Δ_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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