Electron. J. Diff. Equ., Vol. 2013 (2013), No. 255, pp. 1-6.

Lavrent'ev problem for separated flows with an external perturbation

Dmitriy K. Potapov, Victoria V. Yevstafyeva

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.

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Dmitriy K. Potapov
Saint Petersburg State University
7-9, University emb., 199034
St. Petersburg, Russia
email: potapov@apmath.spbu.ru
Victoria V. Yevstafyeva
Saint Petersburg State University
7-9, University emb., 199034
St. Petersburg, Russia
email: vica@apmath.spbu.ru

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