One singularly perturbed system of partial differential equations of the first order (Q1907422)

The authors study the following singularly perturbed system of two linear equations \[ \varepsilon u_t+b_1u_x=a_{11}u+a_{12}v+f,\;v_t+\varepsilon b_2v_x=a_{21}u+ a_{22}v+g \] with homogeneous initial and boundary conditions. The main result is a uniform asymptotics of the solution as \(\varepsilon\to 0\).