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Wave Front Propagation for KPP-Type Equations

  • Mark Freidlin

Abstract

The following equation was considered in [15]:
$$ \frac{{\partial u\left( {t,x} \right)}}{{\partial t}} = \frac{D}{2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} + f\left( u \right),t > 0,x \in {R^1},u\left( {0,x} \right) = \chi - \left( x \right) = \left\{ {\begin{array}{*{20}{c}} {1,x \leqslant 0} \\ {0,x > 0.} \end{array}} \right. $$
(1.1.1)
Here D > 0 and f (u) = c(u)u,where the function c(u) is supposed to be Lipschitz continuous, positive for u < 1 and negative for u > 1, and such that c = c(0) = max0≤u≤1 c(u). Let us denote the class of such functions f (u) by F 1.

Keywords

Convex Hull Markov Process Wave Front Nonlinear Term Wiener Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Mark Freidlin
    • 1
  1. 1.University of MarylandCollege ParkUSA

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