相关论文: Analysis of a spherical free boundary problem mode…
In this paper we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a…
We focus on a highly nonlinear evolutionary abstract PDE system describing volume processes coupled with surfaces processes in thermoviscoelasticity, featuring the quasi-static momentum balance, the equation for the unidirectional evolution…
We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…
In this paper we study a ratio-dependent predator-prey model with a free boundary causing by both prey and predator over a one dimensional habitat. We study the long time behaviors of the two species and prove a spreading-vanishing…
In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. We study the asymptotic behavior of two species evolving in a domain with a free boundary. Sufficient conditions for spreading success and…
We study a nonlocal SIS epidemic model with free boundaries, advection, and spatial heterogeneity, where the dispersal kernels are not assumed to be symmetric. The model describes the evolution of susceptible and infected populations in a…
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular…
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…
This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter…
If a variational problem comes with no boundary conditions prescribed beforehand, and yet these arise as a consequence of the variation process itself, we speak of a free boundary values variational problem. Such is, for instance, the…
We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they…
We consider the classical problem of particle diffusion in $d$-dimensional radially-symmetric systems with absorbing boundaries. A key quantity to characterise such diffusive transport is the evolution of the proportion of particles…
An implicit Euler finite-volume scheme for a parabolic reaction-diffusion system modeling biofilm growth is analyzed and implemented. The system consists of a degenerate-singular diffusion equation for the biomass fraction, which is coupled…
We introduce and analyse a two-sided branching-selection particle system which generalises the well-known $N$-particle branching Brownian motion ($N$-BBM) model, which we call the $(N,p)$-BBM, where either the leftmost or rightmost particle…
Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable…
We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
A dynamical model is proposed to describe the coupled decomposition and profile evolution of a free surface film of a binary mixture. An example is a thin film of a polymer blend on a solid substrate undergoing simultaneous phase separation…