相关论文: A Free Boundary Problem for a Ratio-dependent Pred…

This work presents the existence and uniqueness of solution to a free boundary value problem related to biofilm growth. The problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species…

We are concerned with the nonlinear problem $u_t=u_{xx}+f(u)$, where $f$ is of combustion type, coupled with the Stefan-type free boundary $h(t)$. According to [4,5], for some critical initial data, the transition solution $u$ locally…

This paper is concerned with the study of the behavior of the free boundary for a class of solutions to a one-phase Bernoulli free boundary problem with mixed periodic-Dirichlet boundary conditions. It is shown that if the free boundary of…

A free boundary diffusive logistic model finds application in many different fields from biological invasion to wildfire propagation. However, many of these processes show a random nature and contain uncertainties in the parameters. In this…

At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…

We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free…

We study a sequential estimation problem for an unknown reward in the presence of a random horizon. The reward takes one of two predetermined values which can be inferred from the drift of a Wiener process, which serves as a signal. The…

We perform a detailed analysis of the behaviour of a non-autonomous prey-predator model where age based growth with age discriminatory harvesting in prey and predator's reliance upon alternative food in the absence of that particular prey…

We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to…

One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face $x=0$, variable in time, is considered. Throught several transformations the problem is reduced to a free…

The parabolic obstacle problem for the fractional Laplacian naturally arises in American option models when the assets prices are driven by pure jump L\'evy processes. In this paper we study the regularity of the free boundary. Our main…

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the…

This work analyzes a predator-prey cross-diffusion system coupled with two chemical substances under homogeneous Neumann boundary conditions in a bounded domain Omega subset of R^n (n >= 2) with smooth boundary dOmega. Under appropriate…

A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…

This paper continues to study the monostable cooperative system with nonlocal diffusion and free boundary, which has recently been discussed by [Du and Ni, 2020, arXiv:2010.01244]. We here aim at the four aspects: the first is to give more…

This paper concerns pattern formation in a class of reaction-advection-diffusion systems modeling the population dynamics of two predators and one prey. We consider the biological situation that both predators forage along the population…

We develop an existence and regularity theory for solutions to a geometric free boundary problem motivated by models of tumor growth. In this setting, the tumor invades an accessible region $D$, its motion is directed along a constant…

We consider the free boundary problems of degenerate elliptic equations that describe the level set formulation of the interface motion evolved by anisotropic forced mean curvature flows. The type of free boundary problems in this paper was…

We investigate existence and regularity properties of one-phase free boundary graphs, in connection with the question of whether there exists a complete non-planar free boundary graph in high dimensions.

We derive various novel free boundary problems as limits of a coupled bulk-surface reaction-diffusion system modelling ligand-receptor dynamics on evolving domains. These limiting free boundary problems may be formulated as Stefan-type…