The Behavior as $\varepsilon \to + 0$ of Solutions to $\varepsilon \nabla ^2 w = {{\partial w} / {\partial y}}$ in $| y | \leqq 1$ for Discontinuous Boundary Data

1971 ◽  
Vol 2 (4) ◽  
pp. 567-594 ◽  
Author(s):  
L. Pamela Cook ◽  
G. S. S. Ludford
Keyword(s):  
Boundary Data ◽  
Discontinuous Boundary ◽  
Discontinuous Boundary Data

scholarly journals Second-order elliptic PDEs with discontinuous boundary data

2011 ◽  
Vol 32 (1) ◽  
pp. 48-74 ◽  
Author(s):  
P. Houston ◽  
T. P. Wihler
Keyword(s):  
Boundary Data ◽  
Second Order ◽  
Elliptic Pdes ◽  
Discontinuous Boundary ◽  
Discontinuous Boundary Data

Interaction of fan–jump–fan composite waves in a two-dimensional steady jet for van der Waals gases

2017 ◽  
Vol 14 (01) ◽  
pp. 73-134 ◽  
Author(s):  
Geng Lai
Keyword(s):  
Supersonic Flow ◽  
Van Der Waals ◽  
Wave Interaction ◽  
Goursat Problem ◽  
Two Dimensional ◽  
Interaction Zone ◽  
Simple Waves ◽  
Discontinuous Boundary ◽  
Type Boundary ◽  
Discontinuous Boundary Data

We consider a two-dimensional (2D) steady jet generated by gas streaming in parallel supersonic flow out of a duct and into the atmosphere. When the gas is a van der Waals gas, at the corners at the exit of the duct, the parallel supersonic flow expands symmetrically into centered simple waves, jump–fan (JF) composite waves, fan–jump composite waves, or fan–jump–fan (FJF) composite waves. This paper studies the interaction of the symmetric centered FJF composite waves in the jet. The interaction of the FJF composite waves is more involved in comparison to our earlier work on the interaction of the symmetric centered JF composite waves, since the flow in the FJF composite wave interaction zone is rotational. To construct the flow in the interaction zone, we consider a Goursat-type boundary value problem with discontinuous boundary data associated with the 2D and isentropic steady Euler equations. The existence of a global piecewise smooth solution to this Goursat problem is obtained by a new method based on characteristics.

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