Related papers: A free boundary problem in accretive growth
We study whether the solutions of a parabolic equation with diffusion given by the fractional Laplacian and a dominating gradient term satisfy Dirichlet boundary data in the classical sense or in the generalized sense of viscosity…
We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a…
The Oxygen Depletion problem is an implicit free boundary value problem. The dynamics allow topological changes in the free boundary. We show several mathematical formulations of this model from the literature and give a new formulation…
This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…
This paper deals with a free boundary problem of the Lotka-Volterra type prey-predator model with variable intrinsic growth rate for predator over a one dimensional habitat, in which the free boundary represents the spreading front and is…
In this paper we continue our study of bifurcations of solutions of boundary-value problems for symplectic maps arising as Hamiltonian diffeomorphisms. These have been shown to be connected to catastrophe theory via generating functions and…
We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in…
We consider the dynamics of a Hamiltonian particle forced by a rapidly oscillating potential in $\dim$-dimensional space. As alternative to the established approach of averaging Hamiltonian dynamics by reformulating the system as…
We study the free boundary problem for the flow of a compressible isentropic inviscid elastic fluid. At the free boundary moving with the velocity of the fluid particles the columns of the deformation gradient are tangent to the boundary…
In this paper we study asymptotic behavior of solutions for a free boundary problem modeling the growth of tumors containing two species of cells: proliferating cells and quiescent cells. This tumor model was proposed by Pettet et al in…
We study a free boundary problem modeling multi-layer tumor growth with a small time delay $\tau$, representing the time needed for the cell to complete the replication process. The model consists of two elliptic equations which describe…
This paper considers a mortgage contract where the borrower pays a fixed mortgage rate and has the choice of making prepayment. Assume the market interest follows the CIR model, a free boundary problem is formulated. Here we focus on the…
We classify nontrivial, nonnegative, positively homogeneous solutions of the equation \begin{equation*} \Delta u=\gamma u^{\gamma-1} \end{equation*} in the plane. The problem is motivated by the analysis of the classical Alt-Phillips free…
In this paper, we study the existence of nontrivial solutions of the Dirichlet boundary value problem for the following elliptic system: \begin{equation} \left\{ \begin{aligned} -\Delta u & = au + bv + f(x,u,v); &\quad\mbox{ for…
We consider an ergodic harvesting problem with model ambiguity that arises from biology. To account for the ambiguity, the problem is constructed as a stochastic game with two players: the decision-maker (DM) chooses the `best' harvesting…
This article studies the existence of long-time solutions to the Hamiltonian boundary value problem, and their consistent numerical approximation. Such a boundary value problem is, for example, common in Molecular Dynamics, where one aims…
We develop an existence and regularity theory for a class of degenerate one-phase free boundary problems. In this way we unify the basic theories in free boundary problems like the classical one-phase problem, the obstacle problem, or more…
We explore regularity properties of solutions to a two-phase elliptic free boundary problem near a Neumann fixed boundary in two dimensions. Consider a function u, which is harmonic where it is not zero and satisfies a gradient jump…
A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of…
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…