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Sharp asymptotics for the multidimensional KPP equation

Author

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  • Cohen, Serge
  • Rossignol, Stéphane

Abstract

In this article sharp asymptotics for the solution of nonhomogeneous Kolmogorov, Petrovskii and Pisciunov equation depending on a small parameter are considered when the initial condition is the characteristic function of a set . We show how to extend the Ben Arous and Rouault's result that dealt with d=1 and the initial condition as the characteristic function of A={x[less-than-or-equals, slant]0}. The dependance of the asymptotics on the geometry of the boundary of A is precisely described for the problem with constraints.

Suggested Citation

  • Cohen, Serge & Rossignol, Stéphane, 1999. "Sharp asymptotics for the multidimensional KPP equation," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 237-255, September.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:1:p:237-255
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