Math @ Duke

Publications [#305704] of James H. Nolen
Papers Published
 Nolen, J; Xin, J, A variational principle for KPP front speeds in temporally random shear flows,
Communications in Mathematical Physics, vol. 269 no. 2
(2007),
pp. 493532, ISSN 00103616 [doi]
(last updated on 2017/12/13)
Abstract: We establish the variational principle of KolmogorovPetrovskyPiskunov (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 representation of solutions, and large deviation estimates of the associated stochastic flows. The variational principle then allows us to analytically bound the front speeds. The speed bounds imply the linear growth law in the regime of large root mean square shear amplitude at any fixed temporal correlation length, and the sublinear growth law if the temporal decorrelation is also large enough, the socalled bending phenomenon. © 2006 SpringerVerlag.


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