Finite and infinite speed of propagation for porous medium equations with fractional pressure

We study a porous medium equation with fractional potential pressure: $$\partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u,$$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$. To be specific, the problem is posed for $x\in \mathbb{R}^N$, $N\geq 1$, and $t>0$. The initial data $u(x,0)$ is assumed to be a bounded function with compact support or fast decay at infinity. We establish existence of a class of weak solutions for which we determine whether, depending on the parameter $m$, the property of compact support is conserved in time or not, starting from the result of finite propagation known for $m=2$. We find that when $m\in [1,2)$ the problem has infinite speed of propagation, while for $m\in [2,\infty)$ it has finite speed of propagation. Comparison is made with other nonlinear diffusion models where the results are widely different.Comment: 6 pages, 1 figur

Movimientos sociales, participación y ciudadanía en Andalucía. [Reseña]

Reseña de: ESCALERA REYES, JAVIER y COCA PÉREZ, AGUSTÍN (Coords.) (2013). Movimientos sociales, participación y ciudadanía en Andalucía. Sevilla: Aconcagua Libros, 308 p

Cultura del trabajo jornalera, discurso político y liderazgo: el caso del poder popular de Marinaleda

Sin resume

Humos y sangre. Protestas en la cuenca de las piritas y masacre en Rio Tinto [Reseña]

PÉREZ CEBADA, JUAN DIEGO (2014). Tierra devastada. Historia de la contaminación minera. Madrid: Síntesis; CHASTAGNARED, GERARD (2017). Humos y sangre. Protestas en la cuenca de las piritas y masacre en Rio Tinto (1877-1890). Alicante: Universidad de Alicante