2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120956Using measure-capacity inequalities we study new functional inequalities, namely L^q-Poincaré inequalities and L^q-logarithmic Sobolev inequalities. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media equation for m?1, in terms of L^2-norms and entropies.Analysis of PDEs26D10;35K55;39B62;46E27;46E35;60E15text