相关论文: Stability analysis of hyperbolic-parabolic free bo…
This work addresses the existence and uniqueness of a Wanner-Gujer free-boundary problem that models biofilms under conditions of prevailing detachment. This result significantly extends previous findings in both tumor growth modeling and…
We study the instability of a thin film composed of two miscible fluids (binary fluid) placed on a solid planar surface. We include the fact that both the free surface and wetting energies depend on the mixture concentration. By assuming a…
Biofilms are ubiquitous macro-colonies of bacteria that develop at various interfaces (solid-liquid, solid-gas or liquid-gas). The formation of biofilms starts with the attachment of individual bacteria to an interface, where they…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
In this note we present a survey concerning parabolic free boundary problems involving a discontinuous hysteresis operator. Such problems describe biological and chemical processes "with memory" in which various substances interact…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
Biofilms are bacterial aggregates that grow on moist surfaces. Thin homogeneous biofilms naturally formed on the walls of conducts may serve as biosensors, providing information on the status of microsystems (MEMS) without disrupting them.…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…
We introduce and analyze a model for osmotically spreading biofilm colonies at solid-air interfaces that includes wetting phenomena, i.e. surface forces. The model combines a hydrodynamic description for biologically passive liquid…
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…
We study the free boundary in an unstable parabolic problem arising from a model in combustion. We consider the physical situation in which the heat advances and prove that the free boundary is a $C^{1,\alpha/2}$ hypersurface.
Bacteria invade surfaces by forming dense colonies encased in a polymer matrix. Successful settlement of founder bacteria, early microcolony development and later macroscopic spreading of these biofilms on surfaces rely on complex physical…
We introduce a two-dimensional Hele-Shaw type free boundary model for motility of eukaryotic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion of the cytoskeleton gel (active gel) coupled with…
The global dynamics and regularity of parabolic-hyperbolic systems is an interesting topic in PDEs due to the coupling of competing dissipation and hyperbolic effects. This paper is concerned with the Cauchy problem of a…
Inflow BC plays a critical role in the study of hyperbolic PDE in a bounded domain. We establish $W^{1,\infty}$ stability for 1D hyperbolic conservation laws with inflow data in a bounded interval, and $W^{2,3+}$ stability of a large class…
In this paper, we establish the existence of a positive, bounded solution for a class of parabolic partial differential equations with nonlinear boundary conditions, where the boundary conditions depend on the solution on the boundary at a…
We study diffusion processes that are stopped or reflected on the boundary of a domain. The generator of the process is assumed to contain two parts: the main part that degenerates on the boundary in a direction orthogonal to the boundary…
A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
The mechanical process of progressively debonding an adhesive membrane from a substrate is described as a quasistatic variational evolution of sets and herein investigated. Existence of energetic solutions, based on global minimisers of a…