Chapter 1 is a brief introduction to the concept of a partial differential equation (PDE) with boundary conditions (BCs) that move with time through space (MBPDE). This contrasts with the case of a PDE with BCs that are fixed in space. MBPDEs are an important class of PDEs in applications as illustrated in Chapters 4 and 5.

The discussion in Chapter 1 starts with the statement of the diffusion equation in coordinate-free format that is then specialized to cylindrical coordinates in 3D, then in 1D for subsequent examples in Chapters 2 and 3. A general moving BC is started in terms of the velocity of the moving outer radial boundary.