Related papers: Conservation laws for free-boundary fluid layers
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
We consider the thin-film equation for a class of free boundary conditions modelling friction at the contact line, as introduced by E and Ren. Our analysis focuses on formal long-time asymptotics of solutions in the perfect wetting regime.…
We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the…
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
We study a thermodynamically consistent diffuse-interface model that describes the motion of two macroscopically immiscible, incompressible, and viscous Newtonian fluids with unmatched densities. This model is compatible with continuum…
We consider a one-dimensional free boundary problem governed by a nonlinear diffusion - convection equation with a Neumann condition at fixed face $x=0$, which is variable in time and a like Stefan convective condition on the free boundary.…
In the well-known book of Lions [{\em Mathematical topics in fluid mechanics. Incompressible models}, 1996], global existence results of finite energy weak solutions of the inhomogeneous incompressible Navier-Stokes equations (INS) were…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the…
This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…
We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries.…
We study the Cauchy problem of a $3\times 3$ system of conservation laws modeling two--phase flow of polymer flooding in rough porous media with possibly discontinuous permeability function. The system loses strict hyperbolicity in some…
Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate…
Diffusion of a penetrating liquid in a polymeric material does not often satisfy the classical diffusion equations and requires taking relaxational (viscoelastic) properties of the polymer into account. We investigate a boundary value…
In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero…
A new continuum-mechanical formulation is proposed which encompasses all material processes within and surrounding an ice sheet. Using this formulation, the balance of mass and free-surface relations for ice sheets are derived and…
We consider an incompressible Bingham flow in a thin domain with rough boundary, under the action of given external forces and with no-slip boundary condition on the whole boundary of the domain. In mathematical terms, this problem is…
We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
We investigate how models of fluid properties and boundary conditions influence predictions of convective mixing in confined porous media, with relevance to subsurface carbon dioxide storage. Using high-resolution simulations at high…