An analysis of Time Dependent Coordinate Transformation for Second Order Partial Differential Equation: Boundary Integral Equation Method for Time-Dependent Partial Differential Equations

Abstract

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 coefficients, and the domain does not depend on time.