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We study stationary solutions of the system $u_t=\nabla ((m-1)/m\nabla u^m+u\nabla \phi )$, m => 1, Δφ = ±u, defined in a bounded domain Ω of ${ℝ}^n$. The physical interpretation of the above system comes from the porous medium theory and semiconductor physics.

We study existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions. In this model the evolution of temperature is also taken into account. For stationary states the existence of an external potential is also assumed.

The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak-$L^p$ spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.

We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.

We consider the following problem: $\Delta \Phi =\pm Mover{\int }_{\Omega }{e}^{-\Phi /\Theta }{e}^{-\Phi /\Theta },E=M\Theta \mp 1over2{\int }_{\Omega }{\left|\nabla \Phi \right|}^2{,\Phi |}_{\partial \Omega }=0,$ where Φ: Ω ⊂ ${ℝ}^n$ → ℝ is an unknown function, Θ is an unknown constant and M, E are given parameters.

Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.