相关论文: Existence and uniqueness of solution to a hyperbol…
In this paper a reduced one-dimensional moving boundary model is studied that describes the evolution of a biofilm driven by the presence of a reaction limiting substrate. Global well-posedness is established for the resulting parabolic…
The work presents the analysis of the free boundary value problem related to the invasion model of new species in biofilm reactors. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of…
A free boundary value problem related to the genesis of multispecies granular biofilms is presented. The granular biofilm is modelled as a spherical free boundary domain with radial symmetry. The proposed model is conceived in the framework…
We present the stability analysis of two free boundary problems arising in biofilm modelling. The first, introduced in the 1980s by Wanner and Gujer, is related to the competition between autotrophic and heterotrophic bacteria in a biofilm…
A mathematical model for emerging contaminants sorption in multispecies biofilms, based on a continuum approach and mass conservation principles is presented. Diffusion of contaminants within the biofilm is described using a…
The dynamics of biofilm lifecycle are deeply influenced by the surrounding environment and the interactions between sessile and planktonic phenotypes. Bacterial biofilms typically develop in three distinct stages: attachment of cells to a…
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…
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…
In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic…
In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the…
We show the well-posedness for a large class of degenerate parabolic equations with an additional singularity and mixed Dirichlet-Neumann boundary conditions on bounded Lipschitz domains. The proof is based on an $L^1$-contraction result.…
We perform mathematical anaysis of the biofilm development process. A model describing biomass growth is proposed: It arises from coupling three parabolic nonlinear equations: a biomass equation with degenerate and singular diffusion, a…
We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical…
The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. Our results depend on the size of a parameter that plays the role of the velocity at which mass is…
The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. The equations consist of a reaction-diffusion equation for the substrate concentration and a fourth-order Cahn-Hilliard-type equation…
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion.
A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial…
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 prove an existence result for a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation…
We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting particle…