-total stability and almost periodicity for some partial functional differential equations with infinite delay.
30 Years of Calderón’s Problem
In this article we survey some of the most important developments since the 1980 paper of A.P. Calderón in which he proposed the problem of determining the conductivity of a medium by making voltage and current measurements at the boundary.
A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term.
A boundary integral equation for Calderón's inverse conductivity problem.
Towards a constructive method to determine an L∞-conductivity from the corresponding Dirichlet to Neumann operator, we establish a Fredholm integral equation of the second kind at the boundary of a two dimensional body. We show that this equation depends directly on the measured data and has always a unique solution. This way the geometric optics solutions for the L∞-conductivity problem can be determined in a stable manner at the boundary and outside of the body.
A boundary multivalued integral “equation” approach to the semipermeability problem
The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small...
A boundary value problem for quasilinear hyperbolic systems with a retarded argument
A characterization of families of function sets described by constraints on the gradient
A class age-structured HIV/AIDS model with impulsive drug-treatment strategy.
A class of one-dimensional degenerate parabolic equations
A class of retracts in with some applications to differential inclusion
A class of time discrete schemes for a phase-field system of Penrose-Fife type
A class of time discrete schemes for a phase–field system of Penrose–Fife type
In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.
A Classification of Solutions of Certain Nonlinear Differential Inequalities with Application to Theorems of Liouville Type.
A comparison of multilevel methods for total variation regularization.
A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations
We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium equation, both...
A comparison principle for an American option on several assets: index and spread options.
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand.
A continuity result for a quasilinear elliptic free boundary problem
We investigate a two dimensional quasilinear free boundary problem, and show that the free boundary is a union of graphs of continuous functions.
A difference scheme for an elliptic system of nonlinear differential-functional equations with Dirichlet type boundary conditions. The existence and uniqueness of solution
A directional compactification of the complex Fermi surface and isospectrality