2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165981The convergence to non-diffusive self-similar solutions is investigated for non-negative solutions to the Cauchy problem $\partial_t u = Δ_p u + |\nabla u|^q$ 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 $t\to\infty$.Analysis of PDEs35B40; 35K65; 35K55; 49L25text