The Interior Layer Structure for a Linear Parbolic Problem with Discontinuous Data

We study the initial value problem for a linear parabolic partial differential equation of the form (1.1) L ϵ [ u ϵ ] ≡ ∂ u ϵ ∂ t − ϵ ∂ 2 u ϵ ∂ x 2 + p ( x , t ) ∂ u ϵ ∂ x + q ( x , t ) u ϵ = f ( x , t ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072584/300cbf75-7783-4a6f-9796-7cd4d736d320/content/eq3383.tif"/>