We study the weak solvability of a system of coupled Allen-Cahn-like equations resembling cross-diffusion which is arising as a model for the consolidation of saturated porous media. Besides using energy like estimates, we cast the special structure of the system in the framework of the Leray-Schauder fixed point principle and ensure this way the local existence of strong solutions to a regularised version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.Weak solutions; cross-diffusion system; energy method; Leray-Schauder fixed point theorem; finite differences; consolidation of porous media

In this paper we study the analytic solutions of Burgers type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the timefractional Burgers equation. Some generalizations linked to the forced time-fractional Burgers equations and variable-coefficient diffusion are also considered. Finally we study a Burgers-type equation involving both space and time-fractional derivatives.

The occurrence of heterogeneous perturbations of fluid mass density and solid elastic strain of a porous continuum, as a consequence of its undrained response is a very important topic in theoretical and applied poromechanics. The classical Mandel-Cryer effect provides an explanation of fluid overpressure in the central region of a porous sample, immediately after the application of the loading. However this effect fades away when the fluid leaks out of the porous network. Here this problem is studied within the framework of a second gradient theory and a thorough description of the static and the dynamics of the phenomenon is given. We study how the presence of an impermeable wall affects the formation of the interface between two phases differing in the fluid content. Moreover, we show that the late time interface motion towards its stationary position is not affected by the impermeable wall and is characterized by a common seepage velocity profile

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The mainshocks broke two of the most important extensional fault systems of this portion of the Apennines Mountain belt owning to two different geologic domains: the Mt. Vettore-Mt. Bove fault system (VBFS) to the North, in the Umbria-Marche domain, and the Mt. della Laga fault system (LMFS) to the South, in the Latium-Abruzzi domain. These fault systems are separated by a major regional tectonic structure, the NNE-SSW-trending lateral ramp of the Olevano-Antrodoco-Sibillini (OAS) thrust, inherited from the Miocene-Pliocene compressional tectonic phase (