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Mat. Zametki, 1997, Volume 62, Issue 6, Pages 921–932 (Mi mz1682)  

Boundary value problem for the Burgers system

N. N. Frolov

Far Eastern National University

Abstract: We consider the boundary value problem
$$ \begin{gathered} \operatorname{div}(\rho V)=0,\qquad\rho|_{\Gamma_1}=\rho_0, \rho(V,\nabla V)=\nu\Delta V,\qquad V|_\Gamma=V^0 \end{gathered} $$
for a vector function $V=(V_1,V_2)$ and a scalar function $\rho\ge0$ in a rectangular domain $\Omega\subset\mathbb R^2$ with boundary $\Gamma$. Here
$$ \Gamma_1=\{x\in\Gamma: (V^0,n)<0\},\qquad V_1^0|_\Gamma>0,\qquad\nu=\operatorname{const}>0. $$
We prove that this problem is solvable in Hölder classes.

DOI: https://doi.org/10.4213/mzm1682

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English version:
Mathematical Notes, 1997, 62:6, 771–780

Bibliographic databases:

UDC: 517.9
Received: 21.03.1995
Revised: 27.02.1996

Citation: N. N. Frolov, “Boundary value problem for the Burgers system”, Mat. Zametki, 62:6 (1997), 921–932; Math. Notes, 62:6 (1997), 771–780

Citation in format AMSBIB
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\paper Boundary value problem for the Burgers system
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\pages 921--932
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\jour Math. Notes
\yr 1997
\vol 62
\issue 6
\pages 771--780
\crossref{https://doi.org/10.1007/BF02355467}
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