Lavrent'ev problem for separated flows with an external perturbation

Abstract

We study the Lavrent'ev mathematical model for separated flows with an external perturbation. This model consists of a differential equation with discontinuous nonlinearity and a boundary condition. Using a variational method, we show the existence of a semiregular solution. As a particular case, we study the one-dimensional model.

Keywords

• Lavrent'ev model
• separated flows
• external perturbation
• discontinuous nonlinearity
• semiregular solution
• variational method