We show how some suitable standard energy inequalities can be used for a simple short
derivation of the fundamental supnorm estimate‖ u (⋅, t)‖ L∞(R n)≤ K (n, p)‖ u (⋅, 0) …

We show how to use the L p–L q approach to obtain fundamental estimates for the spatial
supnorm values of solutions u (x, t)=(u 1 (x, t),…, um (x, t)) to general systems of convection …

We consider the large time behavior of solutions for a hyperbolic relaxation system. For a
certain class of initial data the solution is shown to converge to relaxation rarefaction profiles …

We state and discuss a number of fundamental asymptotic properties of solutions u (⋅, t) to
one-dimensional advection–diffusion equations of the form [Formula: see text], x∈ R, t> 0 …

Nous établissons plusieurs propriétés asymptotiques fondamentales des solutions u (⋅, t)
des équations d'avection–diffusion du type u t+ f (u) x=(a (u) ux) x, x∈ R, t> 0, aux données …

In this work we introduce a novel approach to generate lower and upper L2 estimates for
solution derivatives of arbitrary order to a general class of dissipative systems in the case …

In this work the close relation between vorticity and micro-rotation in micropolar flows in Rn
(n= 2 or 3) is identified and used to explain the faster decay by t^(-1/2) of the angular velocity …

In this paper we study the asymptotic behaviour of solutions of certain nonlinear parabolic
equations with variable viscosity and geometric terms. We generalize the results on the …

We derive some basic estimates for supnorm values u (·, t) L∞(R) of bounded weak
solutions to general diffusion equations of the form ut=| u| α uxx+ b (x, t)| u| λ u2 x, x∈ R, t> 0 …

We give a short derivation of supnorm estimates for solutions of onedimensional advection-
diffusion equations () 0,,>∈=+ txu uf u xx xt R and some of their generalizations, assuming …