相关论文: Stability analysis of hyperbolic-parabolic free bo…
In the hyperbolic community, discontinuous Galerkin approaches are mainly applied when finite element methods are considered. As the name suggested, the DG framework allows a discontinuity at the element interfaces, which seems for many…
The bacterium {\em Bacilus subtilis} frequently forms biofilms at the interface between the culture medium and the air. We develop a mathematical model that couples a description of bacteria as individual discrete objects to the standard…
The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was previously proposed by the last three authors. The model…
In this paper, we derive upscaled equations for modelling biofilm growth in porous media. The resulting macro-scale mathematical models consider permeable multi-species biofilm including water flow, transport, detachment and reactions. The…
We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
Bernoulli's free boundary problem is an overdetermined problem in which one seeks an annular domain such that the capacitary potential satisfies an extra boundary condition. There exist two different types of solutions called elliptic and…
We introduce a model concerning radiational gaseous stars and establish the existence theory of stationary solutions to the free boundary problem of hydrostatic equations describing the radiative equilibrium. We also concern the local…
We consider the dynamics of a gas bubble immersed in an incompressible fluid of fixed temperature, and focus on the relaxation of an expanding and contracting spherically symmetric bubble due to thermal effects. We study two models, both…
Bacteria often develop distinct phenotypes to adapt to environmental stress. In particular, they can produce biofilms, dense communities of bacteria that live in a complex extracellular matrix. Bacterial biofilms provide a safe haven from…
We study steady-state thin films on a chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the one-dimensional steady-state solutions that…
This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than that of the ODE. Such a difference of time scales is modeled…
It is an interesting and important topic to study the motion of small particles in a viscous liquid in current applied research. In this paper we assume the particles are convex with arbitrary shapes and mainly investigate the interaction…
We study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown…
Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem…
In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity…
The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…
The goal of this work is to develop a numerical simulation that accurately captures the biomechanical response of bacterial biofilms and their associated extracellular matrix (ECM). In this, the second of a two-part effort, the primary…
We discuss an evolution free boundary problem of mixed type with two free boundaries modeling an idealized electrostatically actuated MEMS device. While the electric potential is the solution of an elliptic equation, the dynamics of the…
Shaking optical lattices in a resonant manner offers an efficient and versatile method to devise artificial gauge fields and topological band structures for ultracold atomic gases. This was recently demonstrated through the experimental…