Related papers: A free boundary problem with facets
This paper is concerned with the long time dynamics of the free boundary of a Darcy fluid in three space dimensions, also known as the one-phase Muskat problem. The dynamics of the free boundary is governed by a nonlocal fully nonlinear…
An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…
We consider viscosity solutions to a one-phase free boundary problem for the $p(x)$-Laplacian with non-zero right hand side. We apply the tools developed in \cite{D} to prove that flat free boundaries are $C^{1,\alpha}$. Moreover, we obtain…
The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a…
We consider a free boundary problem for the $p$-Laplace operator which is related to the so-called Bernoulli free boundary problem. In this formulation, the classical boundary gradient condition is replaced by a condition on the distance…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
In this paper, we present a problem involving fully nonlinear elliptic operators with Hamiltonian, which can present a singularity or degenerate as the gradient approaches the origin. The model studied here, allows the appearance of plateau…
The flow properties at the leading edge of a flat plate represent a singularity to the Blasius laminar boundary layer equations; by applying the Lagrangian approach the leading edge velocity profiles of the laminar boundary layer over a…
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian,…
We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of free boundary to the free boundary of a corresponding…
We study the free boundary in the supercooled Stefan problem, a classical model for the solidification of water below its freezing temperature. In contrast with the melting problem, physical experiments and heuristics indicate that the…
We study the problem of the motion of the free surface of a compressible fluid. We prove existence for the linearized equations.
We extend basic regularity of the free boundary of the obstacle problem to some classes of heterogeneous quasilinear elliptic operators with variable growth that includes, in particular, the $p(x)$-Laplacian. Under the assumption of…
We prove the existence of a solution to an 1-D free boundary problem which describes the propagation of disturbances of shock type, modeled by a non standard variational inequality.
We investigate a class of n-dimensional free boundary elliptic problems which includes the dam problem, the aluminum problem, and the lubrication problem. We establish that the free boundary in this class is a porous set, which implies its…
The free boundary problem for a two-dimensional fluid filtered in porous media is studied. This is known as the one-phase Muskat problem and is mathematically equivalent to the vertical Hele-Shaw problem driven by gravity force. We prove…
Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We…
This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…
We consider a one-phase free boundary problem with variable coefficients and non-zero right hand side. We prove that flat free boundaries are $C^{1,\alpha}$ using a different approach than the classical supconvolution method of Caffarelli.…