Abstract A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem Ritz method. In this process,it may be difficult large system of algebraic equations,the Groebner bases theory (Buchberger’s algorithm) applied problem. The results show that approach much simpler more efficient.

We establish the variational principle of Kolmogorov-Petrovsky-Piskunov (KPP) front speeds in temporally random shear flows with sufficiently decaying correlations. A key quantity in the variational principle is the almost sure Lyapunov exponent of a heat operator with random potential. To prove the variational principle, we use the comparison principle of solutions, the path integral represent...