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The mechanisms leading cells to acquire a fitness advantage and establish themselves in a population are paramount to understanding the development and growth of cancer. Although there are many works that study separately either the…
In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value…
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer…
We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or…
The extra-cellular microenvironment has a fundamental role in tumor growth and progression, strongly affecting the migration strategies adopted by single cancer cells during metastatic invasion. In this study, we use a novel microfluidic…
In this paper, we present a cell motility model that takes into account the cell membrane effect. The model introduced is an incompressible Darcy free boundary problem. This model involves a nonlinear term in the boundary condition to model…
Tumor growth is associated with cell invasion and mass-effect, which are traditionally formulated by mathematical models, namely reaction-diffusion equations and biomechanics. Such models can be personalized based on clinical measurements…
In this paper, we study a nonlinear free boundary problem modeling the growth of spherically symmetric tumors. The tumor consists of a central necrotic core, an intermediate annual quiescent-cell layer, and an outer proliferating-cell…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
We here analyze the propagation of transients of fluid-rock temperature and pressure through a thin boundary layer, where a steady trend is present, between two adjacent homogeneous rocks. We focus on the effect of convection on transients…
We investigate pattern formation in a two-dimensional (2D) Fisher--Stefan model, which involves solving the Fisher--KPP equation on a compactly-supported region with a moving boundary. By combining the Fisher--KPP and classical Stefan…
Dynamic wetting poses a well-known challenge in classical sharp-interface formulation as the no-slip wall condition leads to a contact line singularity that is typically regularized with a Navier boundary condition, often requiring…
Many theoretical and experimental studies suggest that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly…
The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it…
This paper uses linear magnetohydrodynamics to model resonant absorption in coronal plasma with a Cartesian coordinate system. We impose line-tied boundary conditions and tilt the background magnetic field to be oblique to the transition…
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020), 4013--4029], we established the existence and uniqueness…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear.…
In this study, we employ analytical and numerical techniques to examine a phase transition model with moving boundaries. The model displays two relevant spatial scales pointing out to a macroscopic phase and a microscopic phase, interacting…