Geodesic
Boundary value problems for third-order equations with discontinuous coefficient
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 1, pp. 126-138 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $Q=\Omega\times(-T,T)=\{(x,y)\colon x\in\Omega,\ -T$, 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 with variable direction of evolution, equations with discontinuous coefficients.
Mots-clés : equations of composite type 
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V. V. Shubin. Boundary value problems for third-order equations with discontinuous coefficient. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 1, pp. 126-138. http://geodesic.mathdoc.fr/item/VNGU_2012_12_1_a8/

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