3 papers
math.AP2024
The explicit solution of linear, dissipative, second-order initial-boundary value problems with variable coefficients
Matthew Farkas, Bernard Deconinck
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear,…
math.AP2022
Solving the heat equation with variable thermal conductivity
Matthew Farkas, Bernard Deconinck
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we…
math.AP2022
The analytic extension of solutions to initial-boundary value problems outside their domain of definition
Matthew Farkas, Jorge Cisneros, Bernard Deconinck
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transf…