Explicit spatiotemporal response of singular distributed parameter temperature control system

This work presents an efficient nonlinear SDPS model about multi-function building cooling activities. Relevant slow-fast heat conduction process is considered by singular perturbation transformation. And also the spatial nonlinear diffusion property is considered through Laplace operator. On solvability, the explicit state response of SDPS model is addressed with singular system theory and PDE spectrum theory. A clear formulation of temperature spatiotemporal distribution is obtained by Duhamel method.