1. Nonlinear Boundary Value Problems and Simulation of Heat-Electricity Process for Space Nuclear Installations V. A. Galkin, I. V. Galkina Dept. of Applied Mathematics, National Research Nuclear University, IATE, Obninsk, Russia

2. EGE The process of direct transformation of heat energy to electricity is considered for space nuclear reactor. The effect is based on electrons generation on heated emitters in chain of elements (EGE) which are connected in series.

3. EGE structure

4. THERMOEMISSION Uranium is concluded in the metal cover which is the cathode. It is warmed up by nuclear energy to 1600°С. In the backlash filled with cesium of 0,5 mm electrons fly to the anode, at which 600°С. These high temperatures also allow to select from the reactor of more energy and provide the superiority over other similar installations. For comparison we will tell that in thermoelectric converters temperature on the hot party to 1000°С, on cold - to 400°С.

5. The series of EGE

6. The mathematical model of above mentioned phenomenon is based on system of nonlinear boundary - value problems for nonlinear equations

7. Equation for temperature on cathode (boundary-value heat problem on cathode)

8. Theorem 1 For given non-negative flux q(x) and non- negative constants there exists unique non- negative solution of boundary-value heat- cathode problem.

9. The system of equations for the potentials

18. Boundary conditions

19. Space for solution

20. Mapping defined by boundary-value problem

21. Existence and uniqueness theorem