On Fredholm solvability of first boundary value problem for mixed-type second-order equation with spectral parameter

  • Egorov Ivan E., IvanEgorov51@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics, 48 Kulakovsky Street, Yakutsk 677891, Russia
  • Efimova Elena S., OslamE@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics, 48 Kulakovsky Street, Yakutsk 677891, Russia
  • Tikhonova Irina M., irinamikh3007@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics, 48 Kulakovsky Street, Yakutsk 677891, Russia
Keywords: mixed-type equation, a priori estimate, inequality, equality, orthogonality conditions

Abstract

We study the first boundary problem for the mixed-type second-order equation with a spectral parameter in a cylindrical domain in Rn+1. Previously, for the mixed-type second-order equations some results were received only in two-dimensional domains. V. N. Vragov was the first to propose a well-posed statement of a boundary problem for the mixed-type equations. One of the well-posedness conditions is non-negativity of the spectral parameter. Here we analyze the case of complex spectral parameter and receive a priori estimates under certain conditions, using which an existence and uniqueness theorem is proved for the first boundary problem in the energy class. Also, we obtain sufficient conditions for the Fredholm solvability in the energy class.

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How to Cite
Egorov, I., Efimova, E. and Tikhonova, I. ( ) “On Fredholm solvability of first boundary value problem for mixed-type second-order equation with spectral parameter”, Mathematical notes of NEFU, 25(1), pp. 15-24. doi: https://doi.org/10.25587/SVFU.2018.1.12765.
Section
Mathematics