Allen–Cahn and Cahn–Hilliard-like equations for dissipative dynamics of saturated porous media

Abstract

International audienc

Temperature-driven volume transition in hydrogels: Phase-coexistence and interface localization

“…For d = 2, 3, it is possible to get a double well energy. However, we focus on the case d = 1, being dimension one more suitable for setting and solving the interface location problem, through a technique already proposed in different contexts by some of the authors (Cirillo et al, 2009(Cirillo et al, , 2010(Cirillo et al, , 2011(Cirillo et al, , 2012(Cirillo et al, , 2013.…”

Compacton formation under Allen–Cahn dynamics

“…Note that the problem is similar, see also [16][17][18][19], to that of an holonomic conservative mechanical system with Lagrangian coordinate u, not constant mass matrix ε(u), and potential energy of the conservative force −W(u), once the space variable x is interpreted as time. A lot of care has to be used when one wants to exploit this analogy, as the mass matrix ε(u) is not positive defined, but it is equal to zero in the pure phases u = 0 and u = 1.…”

Kink localization under asymmetric double-well potentials

“…For the complete description of the poromechanics setup we refer the readers to [3,7,8,10]. We recall that two fields m, ε : [0, ] → R are introduced having the physical meaning of deviation from a reference value of the fluid density and solid strain, respectively.…”