Phase Transitions and Chapman-Jouguet Combustions

  • Rinaldo M. Colombo
  • Andrea Corli
Conference paper


We consider a system of conservation laws of the form
$$ {{\partial }_{t}}u + {{\partial }_{x}}f(u) = 0, $$
where t ∈ [0,+∞], xR, u ∈ Ω R n and the function f: Ω ↦ R n is smooth. Ω consists of two connected components, called here phases:
$$ \Omega = {{\Omega }_{0}} \cup {{\Omega }_{1}},\quad {{\Omega }_{0}} \cap {{\Omega }_{1}} = \O ,\quad {{\Omega }_{0}} \ne \O ,{{\Omega }_{1}} \ne \O . $$
The system (1) is strictly hyperbolic in Ω and each eigenvalue is either genuinely nonlinear or linearly degenerate.


Cauchy Problem Phase Boundary Riemann Problem Riemann Solver Weak Entropic Solution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Rinaldo M. Colombo
    • 1
  • Andrea Corli
    • 2
  1. 1.Department of MathematicsUniversity of BresciaBresciaItaly
  2. 2.Department of MathematicsUniversity of FerraraFerraraItaly

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