Stability of equilibria for a two-phase osmosis model

For a two-phase moving boundary problem modelling the motion of a semipermeable membrane by osmotic pressure and surface tension, we prove that the manifold of equilibria is locally exponentially attractive. Our method relies on maximal regularity results for parabolic systems with relaxation type boundary dynamics

Fast polarization mechanisms in the uniaxial tungsten-bronze relaxor strontium barium niobate SBN-81

The high-frequency dielectric response of the uniaxial strontium barium niobate crystals with 81% of Sr has been studied from 1 kHz to 30 THz along the polar c axis by means of several techniques (far infrared, time domain terahertz, high-frequency and low-frequency dielectric spectroscopies) in a wide temperature interval 20–600 K. Relaxor properties were observed in the complex dielectric response and four main excitations were ascertained below the phonon frequencies. These fast polarization mechanisms take place at THz, GHz and MHz ranges and show different temperature evolution. The central mode excitation in the THz range, related to anharmonic dynamics of cations, slightly softens from high temperatures and then hardens below T ~ 400 K. Below the phase transition (at T ~ 330 K) an additional microwave excitation appears near 10 GHz related to micro domain wall oscillations. The strongest relaxation appears in the GHz range and slows down on cooling according to the Arrhenius law. Finally, another relaxation, present in the MHz range at high temperatures, also slows down on cooling at least to the kHz range. These two relaxations are due to polar fluctuations and nanodomains dynamics. Altogether, the four excitations explain the dielectric permittivity maximum in the kHz range

Stability of equilibria for a two-phase osmosis model

For a two-phase moving boundary problem modelling the motion of a semipermeable membrane by osmotic pressure and surface tension, we prove that the manifold of equilibria is locally exponentially attractive. Our method relies on maximal regularity results for parabolic systems with relaxation type boundary dynamics. Keywords: Moving boundary problem; Stability; Maximal regularity; Relaxation type boundary dynamic

Well-posedness for a moving boundary model of an evaporation front in a porous medium

\u3cp\u3eWe consider a two-phase elliptic–parabolic moving boundary problem modelling an evaporation front in a porous medium. Our main result is a proof of short-time existence and uniqueness of strong solutions to the corresponding nonlinear evolution problem in an L\u3csup\u3ep\u3c/sup\u3e-setting. It relies critically on nonstandard optimal regularity results for a linear elliptic–parabolic system with dynamic boundary condition.\u3c/p\u3

Classical solutions for a one phase osmosis model

For a moving boundary problem modeling the motion of a semipermeable membrane by osmotic pressure and surface tension, we prove the existence and uniqueness of classical solutions on small time intervals. Moreover, we construct solutions existing on arbitrary long time intervals, provided the initial geometry is close to an equilibrium. In both cases, our method relies on maximal regularity results for parabolic systems with inhomogeneous boundary data

Stability of equilibria of a two-phase Stokes-osmosis problem

Within the framework of variational modelling we derive a two-phase moving boundary problem that describes the motion of a semipermeable membrane separating two viscous liquids in a fixed container. The model includes the effects of osmotic pressure and surface tension of the membrane. For this problem we prove that the manifold of steady states is locally exponentially attractive. Keywords: variational modelling, two-phase Stokes equations, osmosis, moving boundary problem, maximal Lp-regularit

Classical solutions for a one phase osmosis model

For a moving boundary problem modelling the motion of a semipermeable membrane by osmotic pressure and surface tension we prove the existence and uniqueness of classical solutions on small time intervals. Moreover, we construct solutions existing on arbitrary long time intervals, provided the initial geometry is close to an equilibrium. In both cases, our method relies on maximal regularity results for parabolic systems with inhomogeneous boundary data