Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 255, pp. 1-6.

Title: Lavrent'ev problem for separated flows with an external perturbation

Authors: Dmitriy K. Potapov       (Saint Petersburg State Univ, Russia)
         Victoria V. Yevstafyeva  (Saint Petersburg State Univ, Russia)

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.

Submitted July 2, 2013. Published November 20, 2013.
Math Subject Classifications: 35J25, 35J60, 35Q35.
Key Words: Lavrent'ev model; separated flows; external perturbation; 
           discontinuous nonlinearity; semiregular solution; variational method.