The shock location for a class of sensitive boundary value problems (Q1300039)

The paper concerns the internal layer solutions and the exponential sensitivity of the nonlinear singularly perturbed boundary value problem \[ \varepsilon\ddot x=\bigl(g(x) +\delta\bigr)f(\dot x)\;(c<t<d), \] with \(x(c)=A\) and \(x(d)=B\), where the values \(A,B\) are real, while \(\delta,\varepsilon\) are infinitesimal (using E. Nelson's internal set theory), finally \(f,g\) are standard functions satisfying some hypotheses. The results are applied to study the viscous shock location (for the stationary Burgers equation) and the supersonic-subsonic shock that arises in modelling compressible flows.