Characteristic decompositions and boundary value problems for two-dimensional steady relativistic Euler equations

2013 ◽  
Vol 37 (1) ◽  
pp. 136-147 ◽  
Author(s):  
Geng Lai ◽  
Chun Shen
Keyword(s):  
Boundary Value Problems ◽  
Euler Equations ◽  
Boundary Value ◽  
Two Dimensional ◽  
Relativistic Euler Equations

Self-similar solutions of the radially symmetric relativistic Euler equations

2019 ◽  
Vol 31 (6) ◽  
pp. 919-949
Author(s):  
GENG LAI
Keyword(s):  
Boundary Value Problems ◽  
Euler Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Self Similarity ◽  
Relativistic Euler Equations ◽  
Self Similar ◽  
Similar Solutions ◽  
Initial Boundary Value

The study of radially symmetric motion is important for the theory of explosion waves. We construct rigorously self-similar entropy solutions to Riemann initial-boundary value problems for the radially symmetric relativistic Euler equations. We use the assumption of self-similarity to reduce the relativistic Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. For the ultra-relativistic Euler equations, we also obtain the uniqueness of the self-similar entropy solution to the Riemann initial-boundary value problems.

scholarly journals TWO-DIMENSIONAL HYBRIDS WITH MIXED BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 56 (3) ◽  
pp. 245
Author(s):  
Marzena Szajewska ◽  
Agnieszka Tereszkiewicz
Keyword(s):  
Boundary Value Problems ◽  
Special Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Dirichlet Condition ◽  
Two Dimensional ◽  
Neumann Type ◽  
Neumann Boundary Value Problems ◽  
Real Euclidean Space

Boundary value problems are considered on a simplex <em>F</em> in the real Euclidean space R<sup>2</sup>. The recent discovery of new families of special functions, orthogonal on <em>F</em>, makes it possible to consider not only the Dirichlet or Neumann boundary value problems on <em>F</em>, but also the mixed boundary value problem which is a mixture of Dirichlet and Neumann type, ie. on some parts of the boundary of <em>F</em> a Dirichlet condition is fulfilled and on the other Neumann’s works.

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