Boundary integral equation method in rolling contact problems involving roughness, wear and frictional heating

Time-dependent problems with the boundary integral equation method

Time-dependent problems that are modeled by initial-boundary value problems for parabolic or hyperbolic partial differential equations can be treated with the boundary integral equation method. The ideal situation is when the right-hand side in the partial differential equation and the initial conditions vanish, the data are given only on the boundary of the domain, the equation has constant co...

The Boundary Integral Equation Method

Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

Integral Equation Methods for Free Boundary Problems∗

We outline a unified approach for treating free boundary problems arising in Finance using integral equation methods. Starting with the PDE formulations of the free boundary problems, we show how to derive nonlinear integral equations for the free boundaries in a variety of Finance applications. Methods to treat theoretical (existence, uniqueness) questions and analytical and numerical approxim...

Convergence of Time-Stepping Method for Initial and Boundary-Value Frictional Compliant Contact Problems

Beginning with a proof of the existence of a discrete-time trajectory, this paper establishes the convergence of a time-stepping method for solving continuous-time, boundary-value problems for dynamic systems with frictional contacts characterized by local compliance in the normal and tangential directions. Our investigation complements the analysis of the initial-value rigid-body model with on...