Existence and multiplicity of solutions to elliptic problems with discontinuities and free boundary conditions.
Existence and regularity for a minimum problem with free boundary.
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.
Existence of local solutions for free boundary problems for viscous compressible barotropic fluids
We prove the local existence of solutions for equations of motion of a viscous compressible barotropic fluid in a domain bounded by a free surface. The solutions are shown to exist in exactly those function spaces where global solutions were found in our previous papers [14, 15].
Existence of solution for a free boundary problem in a nonlinear piecewise homogeneous medium
Existence of solution to transpiration control problem.
Existence of solutions for the one-phase and the multi-layer free-boundary problems with the -Laplacian operator.
Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Existence results for embedded minimal surfaces of controlled topological type, III
Extension of a regularity result concerning the dam problem
One proves, in the case of piecewise smooth coefficients, that the time derivative of the solution of the so called dam problem is a measure, extending the result proved by the same authors in the case of Lipschitz continuous coefficients.
Finite element approximation of a Stefan problem with degenerate Joule heating
We consider a fully practical finite element approximation of the following degenerate systemsubject to an initial condition on the temperature, , and boundary conditions on both and the electric potential, . In the above is the enthalpy incorporating the latent heat of melting, is the temperature dependent heat conductivity, and is the electrical conductivity. The latter is zero in the frozen zone, , which gives rise to the degeneracy in this Stefan system. In addition to showing stability...
Finite element approximation of a Stefan problem with degenerate Joule heating
We consider a fully practical finite element approximation of the following degenerate system subject to an initial condition on the temperature, u, and boundary conditions on both u and the electric potential, ϕ. In the above p(u) is the enthalpy incorporating the latent heat of melting, α(u) > 0 is the temperature dependent heat conductivity, and σ(u) > 0 is the electrical conductivity. The latter is zero in the frozen zone, u ≤ 0, which gives rise to the degeneracy in this Stefan...
Finite element solution of a nonlinear diffusion problem with a moving boundary
Finite element solution of a nonlinear diffusion problem with a moving boundary
Finite time singularities in transport equations with nonlocal velocities and fluxes
Finite volumes and nonlinear diffusion equations
Forced anisotropic mean curvature flow of graphs in relative geometry
The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
Free boundary problems arising in tumor models
We consider several simple models of tumor growth, described by systems of PDEs, and describe results on existence of solutions and on their asymptotic behavior. The boundary of the tumor region is a free boundary. In §1 the model assumes three types of cells, proliferating, quiescent and necrotic, and the corresponding PDE system consists of elliptic, parabolic and hyperbolic equations. The model in §2 assumes that the tumor has only proliferating cells. Finally in §3 we consider a model for treatment...