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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 1, Pages 126–138
(Mi vngu113)
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This article is cited in 6 scientific papers (total in 6 papers)
Boundary value problems for third-order equations with discontinuous coefficient
V. V. Shubin Novosibirsk State University, Novosibirsk, Russia
Abstract:
In the work we consider boundary value problems for third order equations with changing evolution direction $\operatorname{sign}yu_{yyyy}\pm Au+c(x,y)u= f(x,y)$ in the cylinder $Q=\Omega\times(-T,T)=\{(x,y)\colon x\in\Omega,\ -T<y<T\}$, where $\Omega$ is connected subser of $\mathbb R^n$ that have smooth boundary and $T>0$. Here $A$ is elliptic operator $Au=\frac\partial{\partial x_j}\big(a^{ij}(x)u_{x_i}\big)$. It is assigned boundary conditions on lateral surface $\partial\Omega\times(-T,T)$ of cylinder $Q$ and on bases $\Omega\times\{-T\}$ and $\Omega\times\{T\}$ of cylinder for these equations. Also we assign coupling conditions on section $\Omega\times0$. We prove theorems of existence and uniquness of regular solutions of these problems.
Keywords:
partial differential equations, third-order equations, equations of composite type, equations with variable direction of evolution, equations with discontinuous coefficients.
Received: 04.03.2011
Citation:
V. V. Shubin, “Boundary value problems for third-order equations with discontinuous coefficient”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:1 (2012), 126–138; J. Math. Sci., 198:5 (2014), 637–647
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https://www.mathnet.ru/eng/vngu113 https://www.mathnet.ru/eng/vngu/v12/i1/p126
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Abstract page: | 250 | Full-text PDF : | 94 | References: | 45 | First page: | 11 |
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