Pseudoparabolic and pseudohyperbolic equations in noncylindrical time domains

  • Kozhanov Alexandr I., kozhanov@math.nsc.ru Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk 630090, Russia Novosibirsk State University, 1 Pirogov Street, Novosibirsk 630090, Russia
  • Lukina Galina A., lukina-g@mail.ru Ammosov North-Eastern Federal University, Mirny Polytechnic Institute, 5/1 Tikhonov Street, Mirny 630090, Russia
Keywords: pseudoparabolic equation, pseudohyperbolic equation, noncylindrical domain, boundary value problem, regular solution, existence, uniqueness

Abstract

We study solvability of new boundary value problems for pseudoparabolic and pseudohyperbolic equations with one spatial variable. The solutions for these problems are sought in domains noncylindrical along the time variable, not in the domains with curvilinear borders (domains with moving border) as in the previous works. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives, required in the equation, in the inner subdomains.

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How to Cite
Kozhanov, A. and Lukina, G. (2019) “Pseudoparabolic and pseudohyperbolic equations in noncylindrical time domains”, Mathematical notes of NEFU, 26(3), pp. 15-30. doi: https://doi.org/10.25587/SVFU.2019.17.12.002.
Section
Mathematics