Boundary value problems for third–order pseudoelliptic equations with degeneration

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Boundary value problems for third–order pseudoelliptic equations with degeneration. / Kozhanov, Aleksandr I.

In: Mathematical Notes of NEFU, Vol. 27, No. 3, 2020, p. 16-26.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{764838183a3245d4a290da73ff565627,

title = "Boundary value problems for third–order pseudoelliptic equations with degeneration",

abstract = "We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝn, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x1, …, xn and B is a second-order elliptic operator acting in the same variables x1, …, xn. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev{\textquoteright}s deriva-tives in the equation) are proved for the problems under study.",

keywords = "Degeneration, Elliptic boundary value problem, Existence, Regular solution, Third-order differential equation, Uniqueness",

author = "Kozhanov, {Aleksandr I.}",

year = "2020",

doi = "10.25587/SVFU.2020.63.12.002",

language = "English",

volume = "27",

pages = "16--26",

journal = "Математические заметки СВФУ",

issn = "2411-9326",

publisher = "M. K. Ammosov North-Eastern Federal University",

number = "3",

}

RIS

TY - JOUR

T1 - Boundary value problems for third–order pseudoelliptic equations with degeneration

AU - Kozhanov, Aleksandr I.

PY - 2020

Y1 - 2020

N2 - We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝn, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x1, …, xn and B is a second-order elliptic operator acting in the same variables x1, …, xn. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s deriva-tives in the equation) are proved for the problems under study.

AB - We study the solvability in Sobolev spaces of the Dirichlet problem and other elliptic problems for the differential equations (Formula Presented) x ∈ Ω ⊂ ℝn, t ∈ (0, T), where ∆ if the Laplace operator acting in the variables x1, …, xn and B is a second-order elliptic operator acting in the same variables x1, …, xn. A fea-ture of the equations (∗) is that the sign of the function is not fixed in them. Existence and uniqueness theorems for regular solutions (having all generalized Sobolev’s deriva-tives in the equation) are proved for the problems under study.

KW - Degeneration

KW - Elliptic boundary value problem

KW - Existence

KW - Regular solution

KW - Third-order differential equation

KW - Uniqueness

UR - http://www.scopus.com/inward/record.url?scp=85094846310&partnerID=8YFLogxK

U2 - 10.25587/SVFU.2020.63.12.002

DO - 10.25587/SVFU.2020.63.12.002

M3 - Article

AN - SCOPUS:85094846310

VL - 27

SP - 16

EP - 26

JO - Математические заметки СВФУ

JF - Математические заметки СВФУ

SN - 2411-9326

IS - 3

ER -

ID: 25993792