1. Weakly-nonlinear regimes near the threshold of instability in geothermal systems
Andrey Il’ichev
Steklov Mathematical Institute, Moscow
George Tsypkin
Institute for problems in mechanics, Moscow

2. Geothermal systems
Geometry of the problem; is a high-permeability domain,
1 is a low-permeability domain occupied by water,
2 is the low-permeability domain occupied by vapor,
is the high-permeability domain

3. Equations and boundary conditions
div =0, , ,
div =0, , , , , , , ,
Log , ,

4. Vertical flows

5. Linear stability

6. Long-wave instability

7. KPP equation