ABSTRACT
In this chapter, we study the singular limit for the following nonlinear systems of three equations: https://www.w3.org/1998/Math/MathML"> { u t − u x = 0 , u t − σ ( u , s ) x = 0 , s t + c 1 s x + β s − h ( v ) τ = 0 , https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429127793/23ac7b1a-7507-40d6-a273-6bd6c597433d/content/equ16_0_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> with initial data https://www.w3.org/1998/Math/MathML"> ( v , u , s ) | t = 0 = ( v 0 , u 0 , s 0 ) , https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429127793/23ac7b1a-7507-40d6-a273-6bd6c597433d/content/equ16_0_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where β, τ and c 1 are nonnegative constants. When β = 0, the existence of L2 global weak solution for the Cauchy problem (16.0.1), (16.0.2) is obtained in Section 12.3.
