Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions

• Published in: IMA journal of applied mathematics Vol. 88; no. 4; pp. 525 - 557
• Main Authors: Chaikovskii, Dmitrii, Zhang, Ye
• Format: Journal Article
• Language: English
• Published: Oxford University Press 28.12.2023
• Subjects: reaction–diffusion–advection equation; singular perturbed partial differential equation; inverse source problem; convergence; regularization; asymptotic expansion

Abstract This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction–diffusion–advection equation. By using an asymptotic expansion with the local coordinates in the transition-layer...