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JOURNALS // Sibirskii Matematicheskii Zhurnal // Archive

Sibirsk. Mat. Zh., 2018 Volume 59, Number 5, Pages 1098–1115 (Mi smj3031)

This article is cited in 4 papers

Boundary value problems for odd order forward-backward-type differential equations with two time variables

A. I. Kozhanova, S. V. Potapovab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b North-Eastern Federal University, Institute of Mathematics, Yakutsk, Russia

Abstract: We study solvability of boundary value problems for odd order differential equations in time variables. The presence of a discontinuous alternating coefficient is a peculiarity of these equations. We prove existence and uniqueness theorems for the regular solutions of such an equation, i.e. those that have all Sobolev generalized derivatives entering the equation under study.

Keywords: ultraparabolic equation, forward-backward-type equation, discontinuous coefficients, boundary value problems, existence, uniqueness.

UDC: 517.946

Received: 14.03.2017

DOI: 10.17377/smzh.2018.59.511


 English version:
Siberian Mathematical Journal, 2018, 59:5, 870–884

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© Steklov Math. Inst. of RAS, 2025