A boundary blow-up for sub-linear elliptic problems with a nonlinear gradient term.
A boundary control problem with a nonlinear reaction term.
A Boundary Element Method for a Two-Dimensional Interface Problem in Electromagnetics.
A boundary Harnack principle for infinity-Laplacian and some related results.
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 Connected with Response of Semi-space to a Short Laser Pulse
In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective...
A boundary value problem for an elliptic equation with asymmetric coefficients in a non-schlicht domain.
A boundary value problem for Beltrami differential equation
Solutions to Beltrami differential equation with prescribed boundary correspondence in some plane domains are given.
A boundary value problem for cold plasma dynamics.
A Boundary value Problem for Equations of mixed type
A boundary value problem for mixed-type equations in domains with multiply connected hyperbolicity subdomains.
A boundary value problem for quasilinear hyperbolic systems in the Schauder canonic form
A boundary value problem for quasilinear hyperbolic systems with a retarded argument
A boundary value problem for the wave equation.
A boundary value problem in the hyperbolic space.
A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations
A boundary value problem with multivariables integral type condition for parabolic equations.
A brief introduction to homogenization and miscellaneous applications*
This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of G− or H−convergence. Several applications of the method are given: derivation of Darcy’s law for flows in porous media, derivation of the porosity...
A brief review of some application driven fast algorithms for elliptic partial differential equations
Some application driven fast algorithms developed by the author and his collaborators for elliptic partial differential equations are briefly reviewed here. Subsequent use of the ideas behind development of these algorithms for further development of other algorithms some of which are currently in progress is briefly mentioned. Serial and parallel implementation of these algorithms and their applications to some pure and applied problems are also briefly reviewed.