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 $t\to\infty$.
Reaction diffusion equations with super-linear absorption: universal bounds, uniqueness for the Cauchy problem, boundedness of stationary solutions
On well-posedness of the Cauchy problem for MHD system in Besov spaces
Ultra-analytic effect of Cauchy problem for a class of kinetic equations
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