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

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

2008-07-29

arxiv.org/abs/0807.4657v1

Mathematics

Analysis of PDEs

Scientific paper

The convergence to non-diffusive self-similar solutions is investigated for non-negative solutions to the Cauchy problem $\partial_t u = \Delta_p u + |\nabla u|^q$ 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 $L^\infty$-norm of $u(t)$ converges to a positive value as $t\to\infty$.

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