Related papers: Free transmission problems
We study a transmission problem, in population dynamics, between two juxtaposed habitats. In each habitat, we consider a generalized diffusion equation composed by the Laplace operator and a biharmonic term. We consider that the…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
We find an explicit form of weak solutions to a Riemann problem for a degenerate semilinear parabolic equation with piecewise constant diffusion coefficient. It is demonstrated that the phase transition lines (free boundaries) correspond to…
We investigate some scalar transmission problems between a classical positive material and a negative one, whose physical coefficients are negative. First, we consider cases where the negative inclusion is a disk in 2d and a ball in 3d.…
Linear reaction-diffusion equations with inhomogeneous boundary and transmission conditions are shown to possess the property of maximal Lp regularity. The new feature is the fact that the transmission interface is allowed to intersect the…
This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical…
In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a…
In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock that is driven by a uncertain market status process. The free boundary problem is a variational inequality system of three functions…
A newly developed sharp interface model describes crack propagation by a phase transition process. We solve this free boundary problem numerically and obtain steady state solutions with a self-consistently selected propagation velocity and…
For the system of cold plasma equations describing the motion of electrons in the field of stationary ions, we consider the Riemann problem posed at an impenetrable interface between two media. These media differ in the magnitude of the…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
This paper studies local properties of a two phase free boundary problem for the fractional Laplacian. The main result states that the two free boundaries of the positive and negativity sets cannot touch.
We formulate and study an elliptic transmission-like problem combining local and nonlocal elements. Let $\mathbb{R}^{n}$ be separated into two components by a smooth hypersurface $\Gamma$. On one side of $\Gamma$, a function satisfies a…
In this paper we study a free boundary problem for a ratio-dependent predator-prey system in one space dimension, with the free boundary only caused by the prey. The long time behaviors of solution are discussed. Then we establish a…
In this paper we consider a system of two reaction-diffusion equations that models diffusional-thermal combustion with stepwise ignition-temperature kinetics and fractional reaction order 0 < $\alpha$ < 1. We turn the free interface problem…
We investigate energy and momentum non-contact exchanges between two arbitrary flat media separated by a gap. This problem is revisited as a transmission problem of individual system eigenmodes weighted by a transmission probability…
We consider the transmission problem in presence of interfaces with imperfect bonding. The imperfect bonding condition is characterized by the positive resistance along the interface, which causes discontinuity of the potential across the…
In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain the global existence, uniqueness and longtime behaviour of solution of these two problems. The spreading-vanishing…
The aim of this work is to point out that the class of free boundary problems governed by second order autonomous ordinary differential equations can be transformed to initial value problems. Interest in the numerical solution of free…
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…